11 Angular Momentum
11.3 Conservation of Angular Momentum
Learning Objectives
By the end of this section, you will be able to:
- Apply conservation of angular momentum to determine the angular velocity of a rotating system in which the moment of inertia is changing
- Explain how the rotational kinetic energy changes when a system undergoes changes in both moment of inertia and angular velocity
So far, we have looked at the angular momentum of systems consisting of point particles and rigid bodies. We have also analyzed the torques involved, using the expression that relates the external net torque to the change in angular momentum, Figure. Examples of systems that obey this equation include a freely spinning bicycle tire that slows over time due to torque arising from friction, or the slowing of Earth’s rotation over millions of years due to frictional forces exerted on tidal deformations.
However, suppose there is no net external torque on the system, [latex]\sum \mathbf{\overset{\to }{\tau }}=0.[/latex] In this case, Figure becomes the law of conservation of angular momentum.
Law of Conservation of Angular Momentum
The angular momentum of a system of particles around a point in a fixed inertial reference frame is conserved if there is no net external torque around that point:
or
Note that the total angular momentum [latex]\mathbf{\overset{\to }{L}}[/latex] is conserved. Any of the individual angular momenta can change as long as their sum remains constant. This law is analogous to linear momentum being conserved when the external force on a system is zero.
As an example of conservation of angular momentum, Figure shows an ice skater executing a spin. The net torque on her is very close to zero because there is relatively little friction between her skates and the ice. Also, the friction is exerted very close to the pivot point. Both [latex]|\mathbf{\overset{\to }{F}}|\,\text{and}\,|\mathbf{\overset{\to }{r}}|[/latex] are small, so [latex]|\mathbf{\overset{\to }{\tau }}|[/latex] is negligible. Consequently, she can spin for quite some time. She can also increase her rate of spin by pulling her arms and legs in. Why does pulling her arms and legs in increase her rate of spin? The answer is that her angular momentum is constant, so that
or
where the primed quantities refer to conditions after she has pulled in her arms and reduced her moment of inertia. Because [latex]{I}^{\prime }[/latex] is smaller, the angular velocity [latex]{\omega }^{\prime }[/latex] must increase to keep the angular momentum constant.
It is interesting to see how the rotational kinetic energy of the skater changes when she pulls her arms in. Her initial rotational energy is
whereas her final rotational energy is
Since [latex]{I}^{\prime }{\omega }^{\prime }=I\omega ,[/latex] we can substitute for [latex]{\omega }^{\prime }[/latex] and find
Because her moment of inertia has decreased, [latex]{I}^{\prime } \lt I,[/latex] her final rotational kinetic energy has increased. The source of this additional rotational kinetic energy is the work required to pull her arms inward. Note that the skater’s arms do not move in a perfect circle—they spiral inward. This work causes an increase in the rotational kinetic energy, while her angular momentum remains constant. Since she is in a frictionless environment, no energy escapes the system. Thus, if she were to extend her arms to their original positions, she would rotate at her original angular velocity and her kinetic energy would return to its original value.
The solar system is another example of how conservation of angular momentum works in our universe. Our solar system was born from a huge cloud of gas and dust that initially had rotational energy. Gravitational forces caused the cloud to contract, and the rotation rate increased as a result of conservation of angular momentum (Figure).
We continue our discussion with an example that has applications to engineering.
Example
Coupled Flywheels
A flywheel rotates without friction at an angular velocity [latex]{\omega }_{0}=600\,\text{rev}\text{/}\text{min}[/latex] on a frictionless, vertical shaft of negligible rotational inertia. A second flywheel, which is at rest and has a moment of inertia three times that of the rotating flywheel, is dropped onto it (Figure). Because friction exists between the surfaces, the flywheels very quickly reach the same rotational velocity, after which they spin together. (a) Use the law of conservation of angular momentum to determine the angular velocity [latex]\omega[/latex] of the combination. (b) What fraction of the initial kinetic energy is lost in the coupling of the flywheels?
Strategy
Part (a) is straightforward to solve for the angular velocity of the coupled system. We use the result of (a) to compare the initial and final kinetic energies of the system in part (b).
Solution
a. No external torques act on the system. The force due to friction produces an internal torque, which does not affect the angular momentum of the system. Therefore conservation of angular momentum gives
b. Before contact, only one flywheel is rotating. The rotational kinetic energy of this flywheel is the initial rotational kinetic energy of the system, [latex]\frac{1}{2}{I}_{0}{\omega }_{0}^{2}[/latex]. The final kinetic energy is[latex]\frac{1}{2}(4{I}_{0}){\omega }^{2}=\frac{1}{2}(4{I}_{0}){(\frac{{\omega }_{0}}{4})}^{2}=\frac{1}{8}{I}_{0}{\omega }_{0}^{2}.[/latex]
Therefore, the ratio of the final kinetic energy to the initial kinetic energy is
Thus, 3/4 of the initial kinetic energy is lost to the coupling of the two flywheels.
Significance
Since the rotational inertia of the system increased, the angular velocity decreased, as expected from the law of conservation of angular momentum. In this example, we see that the final kinetic energy of the system has decreased, as energy is lost to the coupling of the flywheels. Compare this to the example of the skater in Figure doing work to bring her arms inward and adding rotational kinetic energy.
Check Your Understanding
A merry-go-round at a playground is rotating at 4.0 rev/min. Three children jump on and increase the moment of inertia of the merry-go-round/children rotating system by [latex]25%[/latex]. What is the new rotation rate?
Show Solution
Using conservation of angular momentum, we have
[latex]I(4.0\,\text{rev/min})=1.25I{\omega }_{\text{f}},\enspace{\omega }_{\text{f}}=\frac{1.0}{1.25}(4.0\,\text{rev}\text{/}\text{min})=3.2\,\text{rev}\text{/}\text{min}[/latex]
Example
Dismount from a High Bar
An 80.0-kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height? See Figure.
Strategy
Using conservation of angular momentum, we can find his rotation rate when in the tuck. Using the equations of kinematics, we can find the time interval from a height of 3.0 m to 1.8 m. Since he is moving horizontally with respect to the ground, the equations of free fall simplify. This will allow the number of revolutions that can be executed to be calculated. Since we are using a ratio, we can keep the units as rev/s and don’t need to convert to radians/s.
Solution
The moment of inertia at full extension is [latex]{I}_{0}=\frac{1}{12}m{L}^{2}=\frac{1}{12}80.0\,\text{kg}(1{.8\,\text{m})}^{2}=21.6\,\text{kg}\cdot {\text{m}}^{2}[/latex].
The moment of inertia in the tuck is [latex]{I}_{\text{f}}=\frac{1}{12}m{L}_{\text{f}}^{\text{2}}=\frac{1}{12}80.0\,\text{kg}(0{.9\,\text{m})}^{2}=5.4\,\text{kg}\cdot {\text{m}}^{2}[/latex].
Conservation of angular momentum: [latex]{I}_{\text{f}}{\omega }_{\text{f}}={I}_{0}{\omega }_{0}\Rightarrow {\omega }_{\text{f}}=\frac{{I}_{0}{\omega }_{0}}{{I}_{\text{f}}}=\frac{21.6\,\text{kg}\cdot {\text{m}}^{2}(1.0\,\text{rev}\text{/}\text{s})}{5.4\,\text{kg}\cdot {\text{m}}^{2}}=4.0\,\text{rev}\text{/}\text{s}[/latex].
Time interval in the tuck: [latex]t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2(3.0-1.8)\text{m}}{9.8\,\text{m}\text{/}\text{s}}}=0.5\,\text{s}[/latex].
In 0.5 s, he will be able to execute two revolutions at 4.0 rev/s.
Significance
Note that the number of revolutions he can complete will depend on how long he is in the air. In the problem, he is exiting the high bar horizontally to the ground. He could also exit at an angle with respect to the ground, giving him more or less time in the air depending on the angle, positive or negative, with respect to the ground. Gymnasts must take this into account when they are executing their dismounts.
Example
Conservation of Angular Momentum of a Collision
A bullet of mass [latex]m=2.0\,\text{g}[/latex] is moving horizontally with a speed of [latex]500.0\,\text{m}\text{/}\text{s}.[/latex] The bullet strikes and becomes embedded in the edge of a solid disk of mass [latex]M=3.2\,\text{kg}[/latex] and radius [latex]R=0.5\,\text{m}\text{.}[/latex] The cylinder is free to rotate around its axis and is initially at rest (Figure). What is the angular velocity of the disk immediately after the bullet is embedded?
Strategy
For the system of the bullet and the cylinder, no external torque acts along the vertical axis through the center of the disk. Thus, the angular momentum along this axis is conserved. The initial angular momentum of the bullet is [latex]mvR[/latex], which is taken about the rotational axis of the disk the moment before the collision. The initial angular momentum of the cylinder is zero. Thus, the net angular momentum of the system is [latex]mvR[/latex]. Since angular momentum is conserved, the initial angular momentum of the system is equal to the angular momentum of the bullet embedded in the disk immediately after impact.
Solution
The initial angular momentum of the system is
The moment of inertia of the system with the bullet embedded in the disk is
The final angular momentum of the system is
Thus, by conservation of angular momentum, [latex]{L}_{i}={L}_{f}[/latex] and
Solving for [latex]{\omega }_{f},[/latex]
Significance
The system is composed of both a point particle and a rigid body. Care must be taken when formulating the angular momentum before and after the collision. Just before impact the angular momentum of the bullet is taken about the rotational axis of the disk.
Summary
- In the absence of external torques, a system’s total angular momentum is conserved. This is the rotational counterpart to linear momentum being conserved when the external force on a system is zero.
- For a rigid body that changes its angular momentum in the absence of a net external torque, conservation of angular momentum gives [latex]{I}_{f}{\omega }_{f}={I}_{i}{\omega }_{i}[/latex]. This equation says that the angular velocity is inversely proportional to the moment of inertia. Thus, if the moment of inertia decreases, the angular velocity must increase to conserve angular momentum.
- Systems containing both point particles and rigid bodies can be analyzed using conservation of angular momentum. The angular momentum of all bodies in the system must be taken about a common axis.
Conceptual Questions
What is the purpose of the small propeller at the back of a helicopter that rotates in the plane perpendicular to the large propeller?
Show Solution
Without the small propeller, the body of the helicopter would rotate in the opposite sense to the large propeller in order to conserve angular momentum. The small propeller exerts a thrust at a distance R from the center of mass of the aircraft to prevent this from happening.
As the rope of a tethered ball winds around a pole, what happens to the angular velocity of the ball?
Show Solution
The angular velocity increases because the moment of inertia is decreasing.
Suppose the polar ice sheets broke free and floated toward Earth’s equator without melting. What would happen to Earth’s angular velocity?
Explain why stars spin faster when they collapse.
More mass is concentrated near the rotational axis, which decreases the moment of inertia causing the star to increase its angular velocity.Show Answer
Competitive divers pull their limbs in and curl up their bodies when they do flips. Just before entering the water, they fully extend their limbs to enter straight down (see below). Explain the effect of both actions on their angular velocities. Also explain the effect on their angular momentum.
Problems
A disk of mass 2.0 kg and radius 60 cm with a small mass of 0.05 kg attached at the edge is rotating at 2.0 rev/s. The small mass suddenly separates from the disk. What is the disk’s final rotation rate?
The Sun’s mass is [latex]2.0\times {10}^{30}\text{kg,}[/latex] its radius is [latex]7.0\times {10}^{5}\,\text{km,}[/latex] and it has a rotational period of approximately 28 days. If the Sun should collapse into a white dwarf of radius [latex]3.5\times {10}^{3}\,\text{km,}[/latex] what would its period be if no mass were ejected and a sphere of uniform density can model the Sun both before and after?
Show Solution
[latex]{L}_{f}=\frac{2}{5}{M}_{S}{(3.5\times {10}^{3}\text{km})}^{2}\frac{2\pi }{{T}_{f}}[/latex],
[latex]\begin{array}{}\\ {(7.0\times {10}^{5}\,\text{km})}^{2}\frac{2\pi }{28\,\text{days}}={(3.5\times {10}^{3}\text{km})}^{2}\frac{2\pi }{{T}_{f}}\Rightarrow {T}_{f}\hfill \\ \\ \\ =28\,\text{days}\frac{{(3.5\times {10}^{3}\text{km})}^{2}}{{(7.0\times {10}^{5}\text{km})}^{2}}=7.0\times {10}^{-4}\text{day}=60.5\,\text{s}\end{array}[/latex]
A cylinder with rotational inertia [latex]{I}_{1}=2.0\,\text{kg}\cdot {\text{m}}^{2}[/latex] rotates clockwise about a vertical axis through its center with angular speed [latex]{\omega }_{1}=5.0\,\text{rad}\text{/}\text{s}.[/latex] A second cylinder with rotational inertia [latex]{I}_{2}=1.0\,\text{kg}\cdot {\text{m}}^{2}[/latex] rotates counterclockwise about the same axis with angular speed [latex]{\omega }_{2}=8.0\,\text{rad}\text{/}\text{s}[/latex]. If the cylinders couple so they have the same rotational axis what is the angular speed of the combination? What percentage of the original kinetic energy is lost to friction?
A diver off the high board imparts an initial rotation with his body fully extended before going into a tuck and executing three back somersaults before hitting the water. If his moment of inertia before the tuck is [latex]16.9\,\text{kg}\cdot {\text{m}}^{2}[/latex] and after the tuck during the somersaults is [latex]4.2\,\text{kg}\cdot {\text{m}}^{2}[/latex], what rotation rate must he impart to his body directly off the board and before the tuck if he takes 1.4 s to execute the somersaults before hitting the water?
Show Solution
[latex]{f}_{\text{f}}=2.1\,\text{rev}\text{/}\text{s}\Rightarrow {f}_{0}=0.5\,\text{rev}\text{/}\text{s}[/latex]
An Earth satellite has its apogee at 2500 km above the surface of Earth and perigee at 500 km above the surface of Earth. At apogee its speed is 730 m/s. What is its speed at perigee? Earth’s radius is 6370 km (see below).
A Molniya orbit is a highly eccentric orbit of a communication satellite so as to provide continuous communications coverage for Scandinavian countries and adjacent Russia. The orbit is positioned so that these countries have the satellite in view for extended periods in time (see below). If a satellite in such an orbit has an apogee at 40,000.0 km as measured from the center of Earth and a velocity of 3.0 km/s, what would be its velocity at perigee measured at 200.0 km altitude?
[latex]{r}_{P}m{v}_{P}={r}_{A}m{v}_{A}\Rightarrow {v}_{P}=18.3\,\text{km}\text{/}\text{s}[/latex]Show Answer
Shown below is a small particle of mass 20 g that is moving at a speed of 10.0 m/s when it collides and sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about its axis through its center and is perpendicular to the page. The cylinder has a mass of 0.5 kg and a radius of 10 cm, and is initially at rest. (a) What is the angular velocity of the system after the collision? (b) How much kinetic energy is lost in the collision?
A bug of mass 0.020 kg is at rest on the edge of a solid cylindrical disk [latex](M=0.10\,\text{kg,}\,R=0.10\,\text{m})[/latex] rotating in a horizontal plane around the vertical axis through its center. The disk is rotating at 10.0 rad/s. The bug crawls to the center of the disk. (a) What is the new angular velocity of the disk? (b) What is the change in the kinetic energy of the system? (c) If the bug crawls back to the outer edge of the disk, what is the angular velocity of the disk then? (d) What is the new kinetic energy of the system? (e) What is the cause of the increase and decrease of kinetic energy?
Show Solution
a. [latex]{I}_{\text{disk}}=5.0\times {10}^{-4}\,\text{kg}\cdot {\text{m}}^{2}[/latex],
[latex]{I}_{\text{bug}}=2.0\times {10}^{-4}\,\text{kg}\cdot {\text{m}}^{2}[/latex],
[latex]\begin{array}{}\\ ({I}_{\text{disk}}+{I}_{\text{bug}}){\omega }_{1}={I}_{\text{disk}}{\omega }_{2},\hfill \\ \\ \\ {\omega }_{2}=14.0\,\text{rad}\text{/}\text{s}\hfill \end{array}[/latex]
b. [latex]\Delta K=0.014\,\text{J}[/latex];
c. [latex]{\omega }_{3}=10.0\,\text{rad}\text{/}\text{s}[/latex] back to the original value;
d. [latex]\frac{1}{2}({I}_{\text{disk}}+{I}_{\text{bug}}){\omega }_{3}^{2}=0.035\,\text{J}[/latex] back to the original value;
e. work of the bug crawling on the disk
A uniform rod of mass 200 g and length 100 cm is free to rotate in a horizontal plane around a fixed vertical axis through its center, perpendicular to its length. Two small beads, each of mass 20 g, are mounted in grooves along the rod. Initially, the two beads are held by catches on opposite sides of the rod’s center, 10 cm from the axis of rotation. With the beads in this position, the rod is rotating with an angular velocity of 10.0 rad/s. When the catches are released, the beads slide outward along the rod. (a) What is the rod’s angular velocity when the beads reach the ends of the rod? (b) What is the rod’s angular velocity if the beads fly off the rod?
A merry-go-round has a radius of 2.0 m and a moment of inertia [latex]300\,\text{kg}\cdot {\text{m}}^{2}.[/latex] A boy of mass 50 kg runs tangent to the rim at a speed of 4.0 m/s and jumps on. If the merry-go-round is initially at rest, what is the angular velocity after the boy jumps on?
Show Solution
[latex]{L}_{\text{i}}=400.0\,\text{kg}\cdot {\text{m}}^{2}\text{/}\text{s}[/latex],
[latex]{L}_{\text{f}}=500.0\,\text{kg}\cdot {\text{m}}^{2}\omega[/latex],
[latex]\omega =0.80\,\text{rad}\text{/}\text{s}[/latex]
A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 22.0-kg child gets onto it by grabbing its outer edge? The child is initially at rest.
Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?
[latex]{I}_{0}=340.48\,\text{kg}\cdot {\text{m}}^{2}[/latex], [latex]{I}_{\text{f}}=268.8\,\text{kg}\cdot {\text{m}}^{2}[/latex], [latex]{\omega }_{\text{f}}=25.33\,\text{rpm}[/latex]Show Answer
(a) Calculate the angular momentum of an ice skater spinning at 6.00 rev/s given his moment of inertia is [latex]0.400\,\text{kg}\cdot {\text{m}}^{2}[/latex]. (b) He reduces his rate of spin (his angular velocity) by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia if his angular velocity decreases to 1.25 rev/s. (c) Suppose instead he keeps his arms in and allows friction of the ice to slow him to 3.00 rev/s. What average torque was exerted if this takes 15.0 s?
Twin skaters approach one another as shown below and lock hands. (a) Calculate their final angular velocity, given each had an initial speed of 2.50 m/s relative to the ice. Each has a mass of 70.0 kg, and each has a center of mass located 0.800 m from their locked hands. You may approximate their moments of inertia to be that of point masses at this radius. (b) Compare the initial kinetic energy and final kinetic energy.
a. [latex]L=280\,\text{kg}\cdot {\text{m}}^{2}\text{/}\text{s}[/latex], [latex]{I}_{\text{f}}=89.6\,\text{kg}\cdot {\text{m}}^{2}[/latex], [latex]{\omega }_{\text{f}}=3.125\,\text{rad}\text{/}\text{s}[/latex]; b. [latex]{K}_{\text{i}}=437.5\,\text{J}[/latex], [latex]{K}_{\text{f}}=437.5\,\text{J}[/latex]Show Answer
A baseball catcher extends his arm straight up to catch a fast ball with a speed of 40 m/s. The baseball is 0.145 kg and the catcher’s arm length is 0.5 m and mass 4.0 kg. (a) What is the angular velocity of the arm immediately after catching the ball as measured from the arm socket? (b) What is the torque applied if the catcher stops the rotation of his arm 0.3 s after catching the ball?
In 2015, in Warsaw, Poland, Olivia Oliver of Nova Scotia broke the world record for being the fastest spinner on ice skates. She achieved a record 342 rev/min, beating the existing Guinness World Record by 34 rotations. If an ice skater extends her arms at that rotation rate, what would be her new rotation rate? Assume she can be approximated by a 45-kg rod that is 1.7 m tall with a radius of 15 cm in the record spin. With her arms stretched take the approximation of a rod of length 130 cm with [latex]10%[/latex] of her body mass aligned perpendicular to the spin axis. Neglect frictional forces.
Show Solution
Moment of inertia in the record spin: [latex]{I}_{0}=0.5\,\text{kg}\cdot {\text{m}}^{2}[/latex],
[latex]{I}_{\text{f}}=1.1\,\text{kg}\cdot {\text{m}}^{2}[/latex],
[latex]{\omega }_{\text{f}}=\frac{{I}_{0}}{{I}_{\text{f}}}{\omega }_{0}\Rightarrow {f}_{\text{f}}=155.5\,\text{rev}\text{/}\text{min}[/latex]
A satellite in a geosynchronous circular orbit is 42,164.0 km from the center of Earth. A small asteroid collides with the satellite sending it into an elliptical orbit of apogee 45,000.0 km. What is the speed of the satellite at apogee? Assume its angular momentum is conserved.
A gymnast does cartwheels along the floor and then launches herself into the air and executes several flips in a tuck while she is airborne. If her moment of inertia when executing the cartwheels is [latex]13.5\,\text{kg}\cdot {\text{m}}^{2}[/latex] and her spin rate is 0.5 rev/s, how many revolutions does she do in the air if her moment of inertia in the tuck is [latex]3.4\,\text{kg}\cdot {\text{m}}^{2}[/latex] and she has 2.0 s to do the flips in the air?
Show Solution
Her spin rate in the air is: [latex]{f}_{\text{f}}=2.0\,\text{rev}\text{/}\text{s}[/latex];
She can do four flips in the air.
The centrifuge at NASA Ames Research Center has a radius of 8.8 m and can produce forces on its payload of 20 gs or 20 times the force of gravity on Earth. (a) What is the angular momentum of a 20-kg payload that experiences 10 gs in the centrifuge? (b) If the driver motor was turned off in (a) and the payload lost 10 kg, what would be its new spin rate, taking into account there are no frictional forces present?
A ride at a carnival has four spokes to which pods are attached that can hold two people. The spokes are each 15 m long and are attached to a central axis. Each spoke has mass 200.0 kg, and the pods each have mass 100.0 kg. If the ride spins at 0.2 rev/s with each pod containing two 50.0-kg children, what is the new spin rate if all the children jump off the ride?
Show Solution
Moment of inertia with all children aboard:
[latex]{I}_{0}=2.4\times {10}^{5}\,\text{kg}\cdot {\text{m}}^{2}[/latex];
[latex]{I}_{\text{f}}=1.5\times {10}^{5}\,\text{kg}\cdot {\text{m}}^{2}[/latex];
[latex]{f}_{\text{f}}=0.3\text{rev}\text{/}\text{s}[/latex]
An ice skater is preparing for a jump with turns and has his arms extended. His moment of inertia is [latex]1.8\,\text{kg}\cdot {\text{m}}^{2}[/latex] while his arms are extended, and he is spinning at 0.5 rev/s. If he launches himself into the air at 9.0 m/s at an angle of [latex]45^\circ[/latex] with respect to the ice, how many revolutions can he execute while airborne if his moment of inertia in the air is [latex]0.5\,\text{kg}\cdot {\text{m}}^{2}[/latex]?
A space station consists of a giant rotating hollow cylinder of mass [latex]{10}^{6}\,\text{kg}[/latex] including people on the station and a radius of 100.00 m. It is rotating in space at 3.30 rev/min in order to produce artificial gravity. If 100 people of an average mass of 65.00 kg spacewalk to an awaiting spaceship, what is the new rotation rate when all the people are off the station?
Show Solution
[latex]{I}_{0}=1.00\times {10}^{10}\,\text{kg}\cdot {\text{m}}^{2}[/latex],
[latex]{I}_{\text{f}}=9.94\times {10}^{9}\,\text{kg}\cdot {\text{m}}^{2}[/latex],
[latex]{f}_{\text{f}}=3.32\,\text{rev}\text{/}\text{min}[/latex]
Neptune has a mass of [latex]1.0\times {10}^{26}\,\text{kg}[/latex] and is [latex]4.5\times {10}^{9}\text{km}[/latex] from the Sun with an orbital period of 165 years. Planetesimals in the outer primordial solar system 4.5 billion years ago coalesced into Neptune over hundreds of millions of years. If the primordial disk that evolved into our present day solar system had a radius of [latex]{10}^{11}[/latex] km and if the matter that made up these planetesimals that later became Neptune was spread out evenly on the edges of it, what was the orbital period of the outer edges of the primordial disk?
Glossary
- law of conservation of angular momentum
- angular momentum is conserved, that is, the initial angular momentum is equal to the final angular momentum when no external torque is applied to the system


The Process of Change
Because health psychology is interested in the psychology behind health-related behaviors, it also concerns itself with how people can learn to change their behaviors. The transtheoretical model of behavior change assesses an individual’s readiness to act on a new healthier behavior, and provides strategies to guide the individual through each stage of the behavior-change process.
Created by Prochaska and DiClemente in the 1970s, the model proposes that change is a process rather than a discrete decision. People must build up the motivation to change and this motivation is dependent on a number of personal and environmental factors. According to the transtheoretical model, behavioral change is a five-step process, consisting of precontemplation, contemplation, preparation, action, and maintenance.


97 Titan and Triton
Learning Objectives
By the end of this section, you will be able to:
- Explain how the thick atmosphere of Titan makes bodies of liquid on its surface possible
- Describe what we learned from the landing on Titan with the Huygens probe
- Discuss the features we observed on the surface of Triton when Voyager 2 flew by
We shift our attention now to small worlds in the more distant parts of the solar system. Saturn’s large moon Titan turns out to be a weird cousin of Earth, with many similarities in spite of frigid temperatures. The Cassini observations of Titan have provided some of the most exciting recent discoveries in planetary science. Neptune’s moon Triton also has unusual characteristics and resembles Pluto, which we will discuss in the following section.
Titan, a Moon with Atmosphere and Hydrocarbon Lakes
Titan, first seen in 1655 by the Dutch astronomer Christiaan Huygens, was the first moon discovered after Galileo saw the four large moons of Jupiter. Titan has roughly the same diameter, mass, and density as Callisto or Ganymede. Presumably it also has a similar composition—about half ice and half rock. However, Titan is unique among moons, with a thick atmosphere and lakes and rivers and falling rain (although these are not composed of water but of hydrocarbons such as ethane and methane, which can stay liquid at the frigid temperatures on Titan).
The 1980 Voyager flyby of Titan determined that the surface density of its atmosphere is four times greater than that on Earth. The atmospheric pressure on this moon is 1.6 bars, higher than that on any other moon and, remarkably, even higher than that of the terrestrial planets Mars and Earth. The atmospheric composition is primarily nitrogen, an important way in which Titan’s atmosphere resembles Earth’s.
Also detected in Titan’s atmosphere were carbon monoxide (CO), hydrocarbons (compounds of hydrogen and carbon) such as methane (CH4), ethane (C2H6), and propane (C3H8), and nitrogen compounds such as hydrogen cyanide (HCN), cyanogen (C2N2), and cyanoacetylene (HC3N). Their presence indicates an active chemistry in which sunlight interacts with atmospheric nitrogen and methane to create a rich mix of organic molecules. There are also multiple layers of hydrocarbon haze and clouds in the atmosphere, as illustrated in Figure 1.
These Voyager discoveries motivated a much more ambitious exploration program using the NASA Cassini Saturn orbiter and a probe to land on Titan called Huygens, built by the European Space Agency. The orbiter, which included several cameras, spectrometers, and a radar imaging system, made dozens of close flybys of Titan between 2004 and 2015, each yielding radar and infrared images of portions of the surface (see Exploring the Outer Planets). The Huygens probe successfully descended by parachute through the atmosphere, photographing the surface from below the clouds, and landing on January 14, 2005. This was the first (and so far the only) spacecraft landing on a moon in the outer solar system.
At the end of its parachute descent, the 319-kilogram Huygens probe safely touched down, slid a short distance, and began sending data back to Earth, including photos and analyses of the atmosphere. It appeared to have landed on a flat, boulder-strewn plain, but both the surface and the boulders were composed of water ice, which is as hard as rock at the temperature of Titan (see Figure 2).
The photos taken during descent showed a variety of features, including drainage channels, suggesting that Huygens had landed on the shore of an ancient hydrocarbon lake. The sky was deep orange, and the brightness of the Sun was a thousand times less than sunlight on Earth (but still more than a hundred times brighter than under the full moon on Earth). Titan’s surface temperature was 94 K (−179 °C). The warmer spacecraft heated enough of the ice where it landed for its instruments to measure released hydrocarbon gas. Measurements on the surface continued for more than an hour before the probe succumbed to the frigid temperature.
Radar and infrared imaging of Titan from the Cassini orbiter gradually built up a picture of a remarkably active surface on this moon, complex and geologically young (Figure 3). There are large methane lakes near the polar regions that interact with the methane in the atmosphere, much as Earth’s water oceans interact with the water vapor in our atmosphere. The presence of many erosional features indicates that atmospheric methane can condense and fall as rain, then flow down valleys to the big lakes. Thus, Titan has a low-temperature equivalent of the water cycle on Earth, with liquid on the surface that evaporates, forms clouds, and then condenses to fall as rain—but on Titan the liquid is a combination of methane, ethane, and a trace of other hydrocarbons. It is a weirdly familiar and yet utterly alien landscape.
These discoveries raise the question of whether there could be life on Titan. Hydrocarbons are fundamental for the formation of the large carbon molecules that are essential to life on our planet. However, the temperature on Titan is far too low for liquid water or for many of the chemical processes that are essential to life as we know it. There remains, though, an intriguing possibility that Titan might have developed a different form of low-temperature carbon-based life that could operate with liquid hydrocarbons playing the role of water. The discovery of such “life as we don’t know it” could be even more exciting than finding life like ours on Mars. If such a truly alien life is present on Titan, its existence would greatly expand our understanding of the nature of life and of habitable environments.
The Cassini mission scientists and the visual presentation specialists at NASA’s Jet Propulsion Laboratory have put together some nice films from the images taken by Cassini and Huygens. See, for example, the Titan approach and the flyover of the Northern lakes district.
Triton and Its Volcanoes
Neptune’s largest moon Triton (don’t get its name confused with Titan) has a diameter of 2720 kilometers and a density of 2.1 g/cm3, indicating that it’s probably composed of about 75% rock mixed with 25% water ice. Measurements indicate that Triton’s surface has the coldest temperature of any of the worlds our robot representatives have visited. Because its reflectivity is so high (about 80%), Triton reflects most of the solar energy that falls on it, resulting in a surface temperature between 35 and 40 K.
The surface material of Triton is made of frozen water, nitrogen, methane, and carbon monoxide. Methane and nitrogen exist as gas in most of the solar system, but they are frozen at Triton’s temperatures. Only a small quantity of nitrogen vapor persists to form an atmosphere. Although the surface pressure of this atmosphere is only 16 millionths of a bar, this is sufficient to support thin haze or cloud layers.
Triton’s surface, like that of many other moons in the outer solar system, reveals a long history of geological evolution (Figure 4). Although some impact craters are found, many regions have been flooded fairly recently by the local version of “lava” (perhaps water or water-ammonia mixtures). There are also mysterious regions of jumbled or mountainous terrain.
The Voyager flyby of Triton took place at a time when the moon’s southern pole was tipped toward the Sun, allowing this part of the surface to enjoy a period of relative warmth. (Remember that “warm” on Triton is still outrageously colder than anything we experience on Earth.) A polar cap covers much of Triton’s southern hemisphere, apparently evaporating along the northern edge. This polar cap may consist of frozen nitrogen that was deposited during the previous winter.
Remarkably, the Voyager images showed that the evaporation of Triton’s polar cap generates geysers or volcanic plumes of nitrogen gas (see Figure 5). (Fountains of such gas rose about 10 kilometers high, visible in the thin atmosphere because dust from the surface rose with them and colored them dark.) These plumes differ from the volcanic plumes of Io in their composition and also in that they derive their energy from sunlight warming the surface rather than from internal heat.
Key Concepts and Summary
Saturn’s moon Titan has an atmosphere that is thicker than that of Earth. There are lakes and rivers of liquid hydrocarbons, and evidence of a cycle of evaporation, condensation, and return to the surface that is similar to the water cycle on Earth (but with liquid methane and ethane). The Cassini-Huygens lander set down on Titan and showed a scene with boulders, made of water ice, frozen harder than rock. Neptune’s cold moon Triton has a very thin atmosphere and nitrogen gas geysers.


Taking Risks
Sarah Parsons
Summer 2019
It is difficult to pinpoint the one thing that sticks out for me about open-pedagogy. I think of it more as the gestalt of teaching — create a space where the number one priority is thinking and learning; hierarchy is not conducive to creating an environment where learning happens; encourage everyone in the learning environment to take chances and stretch themselves beyond what is comfortable and easy; take a risk and keep going; don’t limit knowledge acquisition or demonstrations of mastery to one singular medium; engage teachers, students, and learning on a variety of levels. Trust learners to engage as they can; model behaviors that you want students to emulate – ask questions, be overwhelmed by the experience of learning; stammer; misspeak; miss the mark — do all of these things and keep going — rephrase your thoughts, process out loud, reconsider your earlier statements, have purely beautiful moments of insight and clarity about things that you had not previously considered in full view of your peers and your students. Enjoy learning things you know nothing about, or better yet things that you find distasteful (except Brussel Sprouts which are distasteful always, even with hollandaise sauce). Listen. Admire. Consider what you again what learning and mastery looks like.
For me the challenge is more about creating and sustaining an environment in and out of the classroom where this work is rewarded and respected. My biggest concern about this process is not that I haven’t learned things about how to be a better, more effective educator because I have. Teachers who talk about how to do things differently and how to reconsider our traditional mental and physical model of education always inspire me. My bigger concern is that there are rarely administrators in the room supporting and encouraging the institutional and environmental changes that need to take place in order to make this kind of work our foundation and not a project.


5 Pippa Thorogood McLennan – Measuring use of OERs at Pima Community College through a survey
Goal – To understand the awareness of OERs and their use at Pima Community College through a survey. Data collected from the survey will serve as a baseline for current OER awareness and inform next steps of a strategy to increase use of OERs at Pima Community College.
This activity will support a measurable from the internship to enhance understanding of OER and its impact on the library field, curriculum development, resource management, and student success.
Specific steps – To understand the awareness and use of Open Educational Resources (OERs) at Pima Community College through development of a survey for completion by current students and faculty. The activity will invite current students and faculty at Pima Community College in Fall 2024 semester to complete the survey. The survey will be available through the College’s D2L portal.
The survey is ten questions asking respondents about their current awareness of OER course content at Pima Community College, whether they are undertaking courses with OER course content and any benefits they have found in using OERs.
Collaborators on the development of the survey will be the Pima Community College OER Director, Chelsea James and Fall 2024 semester interns from the University of Arizona. Support to distribute the survey through Pima Community College channels is sought from the College’s D2L Administrator, social media teams and faculty to communicate the availability of the survey. Resources from across OERizona and other OER networks will be consulted to inform question structure and data collection.
To support this activity, engagement and advocacy from faculty and senior staff at Pima Community College is needed to increase awareness of the survey and completion. The activity is dependent on the integrity of the information technology platforms to support the survey format and collection of data which in turn will advise results and reporting. A lack of responses to the survey is a possible barrier to the success of this activity.
The survey be available on Pima Community College’s D2L portal at the end of Fall semester 2024. The end date is yet to be confirmed.
Notes on the process – The activity was discussed within the forum of the University of Arizona interns and OER Director during Fall 2024 semester. Including reasoning for survey, content of survey and how the benefits of the survey will support the other activities. Each activity produced by this semester’s intern group will support the development of the OER strategy at Pima Community College.
Conclusions: This survey is a first step is understanding the awareness and use of OERs at Pima Community College and part of a long term strategy to measure OER use across course content at the College. The results of this survey will be analysed with other statistics gathered at Pima Community College since 2023 on the use of course materials, the affect on cost of course materials on students and graduation rates of students from Pima Community College. The aim is to increase the use of OERs throughout the College’s course content to support student learning, minimise the financial load on students, increase enrolment across all courses at the College and graduation rates. Supporting the College’s commitment of equity and social justice.
Survey here: https://docs.google.com/forms/d/1zMRx5P3ijrdLc6BVzzSzE0bBWlFQlGNHLdaNTsdCBJ4/edit
Supporting Resources:
James, Chelsea (2024) OER updates Fall 2024/Spring 2025 link here: https://docs.google.com/document/d/1zijH7guumrv3ViZp_jR2WNvhy4dT5o9u9Yg_Cwz1neU/edit?tab=t.0#heading=h.pyoameivrjvb
University of Illinois Urbana-Champaign (2023) Open Educational Resources Promotions Guide: Measuring Impact LibGuides link here: https://guides.library.illinois.edu/OERGuide/MeasuringImpact


42
What is emotional intelligence?
Emotional intelligence (otherwise known as emotional quotient or EQ) is the ability to understand, use, and manage your own emotions in positive ways to relieve stress, communicate effectively, empathize with others, overcome challenges and defuse conflict. When it comes to happiness and success in life, emotional intelligence matters just as much as intellectual ability. Emotional intelligence helps you build stronger relationships, succeed at school and work, and achieve your career and personal goals. It can also help you to connect with your feelings, turn intention into action, and make informed decisions about what matters most to you.
Emotional intelligence is commonly defined by four attributes:
- Self-management – You’re able to control impulsive feelings and behaviors, manage your emotions in healthy ways, take initiative, follow through on commitments, and adapt to changing circumstances.
- Self-awareness – You recognize your own emotions and how they affect your thoughts and behavior. You know your strengths and weaknesses, and have self-confidence.
- Social awareness – You have empathy. You can understand the emotions, needs, and concerns of other people, pick up on emotional cues, feel comfortable socially, and recognize the power dynamics in a group or organization.
- Relationship management – You know how to develop and maintain good relationships, communicate clearly, inspire and influence others, work well in a team, and manage conflict.
Why is emotional intelligence so important?
As we know, it’s not the smartest people who are the most successful or the most fulfilled in life. You probably know people who are academically brilliant and yet are socially inept and unsuccessful at work or in their personal relationships. Intellectual ability or your intelligence quotient (IQ) isn’t enough on its own to achieve success in life. Yes, your IQ can help you get into college, but it’s your EQ that will help you manage the stress and emotions when facing your final exams. IQ and EQ exist in tandem and are most effective when they build off one another.
Emotional intelligence affects:
Your performance at school or work. High emotional intelligence can help you navigate the social complexities of the workplace, lead and motivate others, and excel in your career. In fact, when it comes to gauging important job candidates, many companies now rate emotional intelligence as important as technical ability and employ EQ testing before hiring.
Your physical health. If you’re unable to manage your emotions, you are probably not managing your stress either. This can lead to serious health problems. Uncontrolled stress raises blood pressure, suppresses the immune system, increases the risk of heart attacks and strokes, contributes to infertility, and speeds up the aging process. The first step to improving emotional intelligence is to learn how to manage stress.
 Uncontrolled emotions and stress can also impact your mental health, making you vulnerable to anxiety and depression. If you are unable to understand, get comfortable with, or manage your emotions, you’ll also struggle to form strong relationships. This in turn can leave you feeling lonely and isolated and further exacerbate any mental health problems.
Your relationships. By understanding your emotions and how to control them, you’re better able to express how you feel and understand how others are feeling. This allows you to communicate more effectively and forge stronger relationships, both at work and in your personal life.
Your social intelligence.  Social intelligence enables you to recognize friend from foe, measure another person’s interest in you, reduce stress, balance your nervous system through social communication, and feel loved and happy.
Building emotional intelligence: 4 key skills to increasing your EQ
The skills that make up emotional intelligence can be learned at any time. However, it’s important to remember that there is a difference between simply learning about EQ and applying that knowledge to your life. Just because you know you should do something doesn’t mean you will—especially when you become overwhelmed by stress, which can override your best intentions. In order to permanently change behavior in ways that stand up under pressure, you need to learn how to overcome stress in the moment, and in your relationships, in order to remain emotionally aware.
The key skills for building your EQ and improving your ability to manage emotions and connect with others are:
- Self-management
- Self-awareness
- Social awareness
- Relationship management
- Segal, Jeanne Ph.D., Smith, Melinda M.A., Robinson, Lawrence, and Shubin, Jennifer, October 2019, retrieved from: https://www.helpguide.org/articles/mental-health/emotional-intelligence-eq.htm ↵


9.5 Ampère’s Law
LEARNING OBJECTIVES
- Explain how Ampère’s law relates the magnetic field produced by a current to the value of the current
- Calculate the magnetic field from a long straight wire, either thin or thick, by Ampère’s law
A fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative field is one that does the same amount of work on a particle moving between two different points regardless of the path chosen. Magnetic fields do not have such a property. Instead, there is a relationship between the magnetic field and its source, electric current. It is expressed in terms of the line integral of and is known as Ampère’s law. This law can also be derived directly from the Biot-Savart law. We now consider that derivation for the special case of an infinite, straight wire.
Figure 9.5.1shows an arbitrary plane perpendicular to an infinite, straight wire whose current is directed out of the page. The magnetic field lines are circles directed counterclockwise and centered on the wire. To begin, let’s consider over the closed paths and . Notice that one path () encloses the wire, whereas the other () does not. Since the field lines are circular, is the product of and the projection of onto the circle passing through . If the radius of this particular circle is , the projection is , and
(Figure 9.5.1)
With given by Equation 9.3.1,
(9.5.1)
For path , which circulates around the wire, and
(9.5.2)
Path , on the other hand, circulates through both positive (counterclockwise) and negative (clockwise) (see Figure 9.5.1), and since it is closed, . Thus for path ,
(9.5.3)
The extension of this result to the general case is Ampère’s law.
AMPÈRE’S LAW
To determine whether a specific current is positive or negative, curl the fingers of your right hand in the direction of the path of integration, as shown in Figure 9.5.1. If passes through in the same direction as your extended thumb, is positive; if passes through in the direction opposite to your extended thumb, it is negative.
Problem-Solving Strategy: Ampère’s Law
To calculate the magnetic field created from current in wire(s), use the following steps:
- Identify the symmetry of the current in the wire(s). If there is no symmetry, use the Biot-Savart law to determine the magnetic field.
- Determine the direction of the magnetic field created by the wire(s) by right-hand rule 2.
- Chose a path loop where the magnetic field is either constant or zero.
- Calculate the current inside the loop.
- Calculate the line integral around the closed loop.
- Equate with and solve for .
EXAMPLE 9.5.1
Using Ampère’s Law to Calculate the Magnetic Field Due to a Wire
Use Ampère’s law to calculate the magnetic field due to a steady current in an infinitely long, thin, straight wire as shown in Figure 9.5.2.
(Figure 9.5.2)
Strategy
Consider an arbitrary plane perpendicular to the wire, with the current directed out of the page. The possible magnetic field components in this plane, and , are shown at arbitrary points on a circle of radius centred on the wire. Since the field is cylindrically symmetric, neither nor varies with the position on this circle. Also from symmetry, the radial lines, if they exist, must be directed either all inward or all outward from the wire. This means, however, that there must be a net magnetic flux across an arbitrary cylinder concentric with the wire. The radial component of the magnetic field must be zero because . Therefore, we can apply Ampère’s law to the circular path as shown.
Solution
Over this path is constant and parallel to , so
Thus Ampère’s law reduces to
Finally, since is the only component of we can drop the subscript and write
This agrees with the Biot-Savart calculation above.
Significance
Ampère’s law works well if you have a path to integrate over which has results that are easy to simplify. For the infinite wire, this works easily with a path that is circular around the wire so that the magnetic field factors out of the integration. If the path dependence looks complicated, you can always go back to the Biot-Savart law and use that to find the magnetic field.
EXAMPLE 9.5.2
Calculating the Magnetic Field of a Thick Wire with Ampère’s Law
The radius of the long, straight wire of Figure 9.5.3 is , and the wire carries a current that is distributed uniformly over its cross-section. Find the magnetic field both inside and outside the wire.
(Figure 9.5.3)
Strategy
This problem has the same geometry as Example 9.5.1, but the enclosed current changes as we move the integration path from outside the wire to inside the wire, where it doesn’t capture the entire current enclosed (see Figure 9.5.3).
Solution
For any circular path of radius that is centered on the wire,
From Ampère’s law, this equals the total current passing through any surface bounded by the path of integration.
Consider first a circular path that is inside the wire such as that shown in part (a) of Figure 9.5.3. We need the current passing through the area enclosed by the path. It’s equal to the current density times the area enclosed. Since the current is uniform, the current density inside the path equals the current density in the whole wire, which is . Therefore the current passing through the area enclosed by the path is
We can consider this ratio because the current density is constant over the area of the wire. Therefore, the current density of a part of the wire is equal to the current density in the whole area. Using Ampère’s law, we obtain
and the magnetic field inside the wire is
Outside the wire, the situation is identical to that of the infinite thin wire of the previous example; that is,
The variation of with is shown in Figure 9.5.4.
(Figure 9.5.4)
Significance
The results show that as the radial distance increases inside the thick wire, the magnetic field increases from zero to a familiar value of the magnetic field of a thin wire. Outside the wire, the field drops off regardless of whether it was a thick or thin wire.
This result is similar to how Gauss’s law for electrical charges behaves inside a uniform charge distribution, except that Gauss’s law for electrical charges has a uniform volume distribution of charge, whereas Ampère’s law here has a uniform area of current distribution. Also, the drop-off outside the thick wire is similar to how an electric field drops off outside of a linear charge distribution, since the two cases have the same geometry and neither case depends on the configuration of charges or currents once the loop is outside the distribution.
EXAMPLE 9.5.3
Using Ampère’s Law with Arbitrary Paths
Use Ampère’s law to evaluate for the current configurations and paths in Figure 9.5.5.
(Figure 9.5.5)
Strategy
Ampère’s law states that where is the total current passing through the enclosed loop. The quickest way to evaluate the integral is to calculate by finding the net current through the loop. Positive currents flow with your right-hand thumb if your fingers wrap around in the direction of the loop. This will tell us the sign of the answer.
Solution
(a) The current going downward through the loop equals the current going out of the loop, so the net current is zero. Thus, .
(b) The only current to consider in this problem is because it is the only current inside the loop. The right-hand rule shows us the current going downward through the loop is in the positive direction. Therefore, the answer is .
(c) The right-hand rule shows us the current going downward through the loop is in the positive direction. There are of current going downward and going upward. Therefore, the total current is and .
Significance
If the currents all wrapped around so that the same current went into the loop and out of the loop, the net current would be zero and no magnetic field would be present. This is why wires are very close to each other in an electrical cord. The currents flowing toward a device and away from a device in a wire equal zero total current flow through an Ampère loop around these wires. Therefore, no stray magnetic fields can be present from cords carrying current.
CHECK YOUR UNDERSTANDING 9.6
Consider using Ampère’s law to calculate the magnetic fields of a finite straight wire and of a circular loop of wire. Why is it not useful for these calculations?
Candela Citations
- Download for free at<EMAIL_ADDRESS>Retrieved from<EMAIL_ADDRESS>License: CC BY: Attribution


Learning Objectives
Understand the structure and function of smooth muscle tissue
By the end of this section, you will be able to:
- Understand the difference between single-unit and multi-unit smooth muscle
- Describe the microanatomy of a smooth muscle cell
- Explain the process of smooth muscle contraction
- Explain how smooth muscle differs from skeletal muscle
Smooth muscle, so-named because the cells do not have visible striations, is present in the walls of hollow organs (e.g., urinary bladder), lining the blood vessels, and in the eye (e.g., iris) and skin (e.g., erector pili muscle). Smooth muscle displays involuntary control and can be triggered via hormones, neural stimulation by the ANS, and local factors. In certain locations, such as the walls of visceral organs, stretching the muscle can trigger its contraction).
Smooth muscle fibers are spindle-shaped and, unlike skeletal muscle fibers, have a single nucleus; individual cells range in size from 30 to 200 μm. Smooth muscle fibers are often found forming sheets of tissue and function in a coordinated fashion due to the presence of gap junctions between the cells. Termed unitary smooth muscle or visceral muscle, this type of smooth muscle is the most common observed in the human body, forming the walls of hollow organs. Single-unit smooth muscle produces slow, steady contractions that allow substances, such as food in the digestive tract, to move through the body.
Multi-unit smooth muscle, the second type of smooth muscle observed, are composed of cells that rarely possess gap junctions, and thus are not electrically coupled. As a result, contraction does not spread from one cell to the next, but is instead confined to the cell that was originally stimulated. This type of smooth muscle is observed in the large airways to the lungs, in the large arteries, the arrector pili muscles associated with hair follicles, and the internal eye muscles which regulate light entry and lens shape.
External Website
View the University of Michigan WebScope at http://virtualslides.med.umich.edu/Histology/Digestive%20System/Intestines/169_HISTO_40X.svs/view.apml to explore the tissue sample in greater detail.
Although smooth muscle cells do not have striations, smooth muscle fibers do have actin and myosin contractile proteins which interact to generate tension. These fibers are not arranged in orderly sarcomeres (hence, no striations) but instead are anchored to dense bodies which are scattered throughout the cytoplasm and anchored to the sarcolemma. A network of intermediate fibers run between the dense bodies providing an internal framework for contractile proteins to work against.
A dense body is analogous to the Z-discs of skeletal muscle, anchoring the thin filaments in position. Calcium ions are supplied primarily from the extracellular environment. T-tubules are absent but small indentations, called calveoli, in the sarcolemma represent locations where there are a high density of calcium channels present to facilitate calcium entry. Sarcoplasmic reticulum is present in the fibers but is less developed than that observed in skeletal muscle.
Because smooth muscle cells do not contain troponin, cross-bridge formation is not regulated by the troponin-tropomyosin complex but instead by the regulatory protein calmodulin. When a smooth muscle cell is stimulated, external Ca++ ions passing through opened calcium channels in the sarcolemma, with additional Ca++ released by the sarcoplasmic reticulum. Calcium binds to calmodulin in the cytoplasm with the Ca++-calmodulin complex then activating an enzyme called myosin (light chain) kinase. Myosin light chain kinase in turn, activates the myosin heads by phosphorylating them (converting ATP to ADP and Pi, with the Pi attaching to the head). The heads can then attach to actin-binding sites and pull on the thin filaments.
When the thin filaments slide past the thick filaments, they pull on the dense bodies, which then pull on the intermediate filaments networks throughout the sarcoplasm. This arrangement causes the entire muscle fiber to contract in a manner whereby the ends are pulled toward the center, causing the midsection to bulge in a corkscrew motion (Figure 10.7.2).
Muscle contraction continues until ATP-dependent calcium pumps actively transport Ca++ ions out of the cell or back into the sarcoplasmic reticulum. However, a low concentration of calcium remains in the sarcoplasm to maintain muscle tone. This remaining calcium keeps the muscle slightly contracted, which is important in certain functions, such as maintaining pressure in blood vessels.
Because most smooth muscles must function for long periods without rest, their power output is relatively low to minimize energy needs. Some smooth muscle can also maintain contractions even as Ca++ is removed and myosin kinase is inactivated/dephosphorylated. This can happen as a subset of cross-bridges between myosin heads and actin, called latch-bridges, keep the thick and thin filaments linked together for a prolonged period, without the need for ATP. This allows for the maintaining of muscle “tone” in smooth muscle that lines arterioles and other visceral organs with very little energy expenditure.
For smooth muscle stimulated by neurons, the axons from autonomic nervous system neurons do not form the highly organized neuromuscular junctions as observed in skeletal muscle. Instead, there is a series of neurotransmitter-filled bulges, called varicosities, along the axon of the neuron feeding the smooth muscle that release neurotransmitters over a wide synaptic cleft. Also, visceral muscle in the walls of the hollow organs (except the heart) contains pacesetter cells. A pacesetter cell can spontaneously trigger action potentials and contractions in the muscle.
Hyperplasia in Smooth Muscle
Similar to skeletal muscle cells, smooth muscle can undergo hypertrophy to increase in size. Unlike other muscle, smooth muscle will also divide quite readily to produce more cells, a process called hyperplasia. This can most evidently be observed in the uterus at puberty, which responds to increased estrogen levels by producing more uterine smooth muscle fibers.
Sections Summary
Smooth muscle is found throughout the body around various organs and tracts. Smooth muscle cells have a single nucleus, and are spindle-shaped. Smooth muscle cells can undergo hyperplasia, mitotically dividing to produce new cells. The smooth cells are nonstriated, but their sarcoplasm is filled with actin and myosin, along with dense bodies in the sarcolemma to anchor the thin filaments and a network of intermediate filaments involved in pulling the sarcolemma toward the fiber’s middle, shortening it in the process. Ca++ ions trigger contraction when they are released from SR and enter through opened voltage-gated calcium channels. Smooth muscle contraction is initiated when the Ca++ binds to intracellular calmodulin, which then activates an enzyme called myosin kinase that phosphorylates myosin heads so they can form the cross-bridges with actin and then pull on the thin filaments. Smooth muscle can be stimulated by pacesetter cells, by the autonomic nervous system, by hormones, spontaneously, or by stretching. The fibers in some smooth muscle have latch-bridges, cross-bridges that cycle slowly without the need for ATP; these muscles can maintain low-level contractions for long periods. Single-unit smooth muscle tissue contains gap junctions to synchronize membrane depolarization and contractions so that the muscle contracts as a single unit. Single-unit smooth muscle in the walls of the viscera, called visceral muscle, has a stress-relaxation response that permits muscle to stretch, contract, and relax as the organ expands. Multiunit smooth muscle cells do not possess gap junctions, and contraction does not spread from one cell to the next.
Review Questions
Critical Thinking Questions
1. Why can smooth muscles contract over a wider range of resting lengths than skeletal and cardiac muscle?
2. Describe the differences between single-unit smooth muscle and multiunit smooth muscle.
Glossary
- calmodulin
- regulatory protein that facilitates contraction in smooth muscles
- dense body
- sarcoplasmic structure that attaches to the sarcolemma and shortens the muscle as thin filaments slide past thick filaments
- hyperplasia
- process in which one cell splits to produce new cells
- latch-bridges
- subset of a cross-bridge in which actin and myosin remain locked together
- pacesetter cell
- cell that triggers action potentials in smooth muscle
- stress-relaxation response
- relaxation of smooth muscle tissue after being stretched
- varicosity
- enlargement of neurons that release neurotransmitters into synaptic clefts
- visceral muscle
- smooth muscle found in the walls of visceral organs
Solutions
Answers for Critical Thinking Questions
- Smooth muscles can contract over a wider range of resting lengths because the actin and myosin filaments in smooth muscle are not as rigidly organized as those in skeletal and cardiac muscle.
- Single-unit smooth muscle is found in the walls of hollow organs; multiunit smooth muscle is found in airways to the lungs and large arteries. Single-unit smooth muscle cells contract synchronously, they are coupled by gap junctions, and they exhibit spontaneous action potential. Multiunit smooth cells lack gap junctions, and their contractions are not synchronous.
This work, Anatomy & Physiology, is adapted from Anatomy & Physiology by OpenStax, licensed under CC BY. This edition, with revised content and artwork, is licensed under CC BY-SA except where otherwise noted.
Images, from Anatomy & Physiology by OpenStax, are licensed under CC BY except where otherwise noted.
Access the original for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction.


Argumentation
“Fake news” is a phrase you’ve encountered way more than you would have liked since the 2016 U.S. presidential election. While this phrase has gained more and more momentum and traction, it holds different purposes and meanings in different contexts. Across all these different rhetorical situations, though, we can agree that the popularization of the phrase speaks to an increased skepticism toward the bodies of knowledge that surround us.Such distrust points to the oversimplified dichotomy of fact vs. opinion. The gray area between fact and opinion is much broader than we like to believe, and often we present deeply entrenched opinions as if they were facts. (Whether or not it is intentional, this phenomenon has serious consequences.) As Michael Kinsley points out in his 1995 essay, American individualist ideology dictates that citizens be “omni-opinionated” – at the expense of having many poorly informed opinions. It is crucial, Kinsley says that we take two steps to confront the “intellectual free lunch”:
- Develop increased humility about what we can and do know to be true; and
- Increase the intensity and frequency of our critical interrogation of truth (or what seems to be true).
Because, yes, there is a lot of fake news out there. And there’s a lot of real news that certain people insist is fake. How do we mobilize skepticism to produce a more ethical world rather than letting it undermine the pursuit of truth?
 It surfaces connotations of raised voices, slammed doors, and dominance; it arouses feelings of anxiety and frustration. But argument is not inherently bad. In fact, as a number of great thinkers have described, conflict is necessary for growth, progress, and community cohesion. Through disagreement, we challenge our common sense assumptions and seek compromise. The negative connotations surrounding ‘argument’ actually point to a failure in the way that we argue.
Check out this video on empathy. It provides useful insight into the listening, thinking, and discussion required for productive arguments.


18 Use the Pomodoro Method to Get Started
A key aspect of overcoming procrastination is developing strategies to get started. Often, committing to complete one small task can be enough to begin moving ahead. For example, just taking out your laptop, creating a document, and typing the title can create some forward momentum.
A well-known technique for managing time that can help with procrastination is called the Pomodoro Technique. This technique is a method of managing procrastination by breaking down your work periods into small, manageable units. This video explains how the Pomodoro technique can work for you. After watching the video, you’ll test your new knowledge with a short quiz.
Video Transcript
Welcome back. Let’s pick up where we left off. You had made a commitment to make one small change and had written it down with a date to make your goal timely. Good for you!
Now I would like to share a technique that has worked for me.
Have you ever heard of the Pomodoro Technique? Take a look at this cute little kitchen timer. How could something like this help you?
The technique has been around for a while and I have used it to help in a critical point in my studies. I was completing an individual studies project.  It is the perfect kind of course to go and explore new ideas but it is also a course that takes a lot of self-directed effort and procrastination can lead to failure. Unfortunately, I was going down that failure road. So I applied all my learning strategies and nothing that I had learned to that point really helped me. I knew why I was procrastinating. I knew that I should divide my tasks into chunks. I had talked it over with my mentors. But still the procrastination continued. I wanted a change.
The pomodoro (or tomato) description was used because the inventor of this technique (Francesco Cirillo) first used his mother’s kitchen timer, which looked like a pretty red tomato, to set aside chunks of time to work with focus on one part of a task. This gets to the basics of dealing with the procrastination monster, divide your task into small chunks, baby steps, and work to complete the steps.
A word of warning… Do NOT use your phone to time you. What will probably happen is that you will get distracted from your work and start using social media or Youtube. Technology can be our friend, but if you have a big problem with procrastination, you must put your phone down and concentrate on your task.
So in a nutshell here is the technique that saved my degree and allowed me to be here, at KPU serving you.
Step One: Choose the task
Step Two: Set the timer for 25 minutes- no interruptions are allowed! Turn off your phone
Step Three: Work until the timer rings- put a check mark on the paper
Step Four: Take a short break
Step Five: Do up to 4 pomodoros and then take a longer break.
So give it a try…because it may work well for you and save you from a lot of problems. Of course if you want more structured help, please come to see me or one of our other learning strategists. We can help you pull all of this information together.
We welcome all feedback, so if you can answer a few questions, it will help us to serve you better.
Good luck and I’ll see you soon in the KPU Learning Centre.


9.1 Building Confidence as a Presenter
Monika Smith and Suzan Last
“Even the greatest was once a beginner.”
Muhammad Ali
“All the great speakers were bad speakers at first.”
Ralph Waldo Emerson
In this section, you will find some practical steps for becoming an effective public speaker, based on the principle that no matter how much of a novice or an expert you are, there’s always something to learn and room to improve. If you feel anxious about speaking in front of others—and, admittedly, most people do—then the steps, information, and additional resources provided here will help build your confidence, give you some stage tools to work with, and direct you to resources to further solidify your learning.
Before you begin the process of building skills, watch the video below, How I Overcame My Fear of Public Speaking (2017) by Danish Dhamani, then consider the preliminary steps that follow.
Knowledge Check
1. Acknowledge the Challenge: The first thing to acknowledge up front is that, aside from extroverts (a minority of the population), most people dislike, if not actively shudder at, the idea of public speaking. For many people, even those who have to speak as part of their job, the mere thought of speaking in front of a crowd can evoke feelings of doom and gloom: furrowed brows, shaking hands, trembling voice, and palpitations.
Figures from a range of sources show you’re in good company:
- From a 2015 Canadian Cancer Society survey: 33% of the 1500 people surveyed feared public speaking the most.
- From a Statistic Brain survey quoted in Forbes: 74% of people suffer from a fear of public speaking (Zimmerman, 2017).
Hence, if you’d like to become an effective public speaker but feel anxious at the prospect of actually doing public speaking, you’re not alone. Your fear of public speaking isn’t a personal failing; it’s a common human response.
The good news, of course, is that fear of public speaking can be overcome. Some of the most famous voices we know initially struggled as speakers: James Earl Jones, the voice of Darth Vader in Star Wars, overcame tremendous personal and social anxieties to “find his voice” and in doing so, got to the point where he could comfortably and confidently speak up and speak out (Jones & Niven, 1993). You can too.
2. Recognize the Costs and Benefits: Acknowledge the personal and professional costs of remaining stuck and not tackling the challenge that speaking before others can pose. Unfortunately, even if employees have strong technical skills, an admirable work ethic, and intelligent, innovative ideas, if they struggle to speak confidently and coherently in a public or workplace setting, they may find it difficult to make a strong positive impact. For example, fear of public speaking can
- lead people to believe they’re less competent and worthy than they are,
- keep their ideas from being heard and acted on, and
- become a glass ceiling in their own career and thwarting advancement.
Being unable to persuasively communicate your ideas in front of a group or audience means that, more likely than not, your ideas, skills, and potential—qualities that could have helped solve a problem and made a positive impact—don’t get heard.
All these negatives stand in sharp contrast to what can be achieved with a strong, persuasive, confident voice. Once you commit to developing your voice as a presenter, you’ll find that speaking up is both liberating and empowering: It not only allows your ideas to be heard, it enables you to accomplish the goals you set. Putting effort into developing your professional speaking skills will pay off in the long run, maximizing your potential as a professional.
3. Commit to Learning: Whether public speaking makes you anxious or whether you enjoy taking center stage, everyone can learn how to become a better public speaker. Regardless of where you are on the public speaking spectrum, you can always develop your skills by learning about and practicing the tips, techniques, and strategies that successful public speakers use to inform, persuade, and even inspire their audiences.
4. Commit to Thorough Preparation: Whether you are presenting to a small group at a workplace meeting or to a larger crowd at a conference, completing a thorough preparation will help to build your confidence in the material you will be presenting. Knowing your materials will help to lessen your anxiety and allow you to take some pleasure in the speaking experience.
You may be interested in reading more about overcoming presentation anxiety. Michael J. Gelb, in Mastering the Art of Public Speaking (2020), offers a lively, straightforward “how-to” approach to public speaking, paying special attention to how to overcome your fears and feel more confident. In short, it’s all about preparation.
Knowledge Check
References
Canadian Cancer Society. (2015, June 8). Snakes and ladders top list of Canadians’ fears, just don’t ask them to speak publicly about it. https://www.newswire.ca/news-releases/snakes-and-ladders-top-list-of-canadians-fears-just-dont-ask-them-to-speak-publicly-about-it-517896421
Dhamani, D. (2017, December 15). How I overcame my fear of public speaking. [Video]. YouTube. https://youtu.be/80UVjkcxGmA
Gelb, M.J. (2020). Mastering the art of public speaking: 8 secrets to transform fear and supercharge your career. Novato, CA: New World Library.
Jones, J. E. & Niven, P. (1993). James Earl Jones: Voices of silence. New York: Scribner Book Co.
TED Masterclass. (n.d.). “The #1 rule for improving your presentation slides” TED.com, https://www.ted.com/about/programs-initiatives/ted-masterclass
Zimmerman, K. (2017, February 8). 4 reasons all millennials should develop their public speaking skills. Forbes. https://www.forbes.com/sites/kaytiezimmerman/2017/02/08/4-reasons-all-millennials-should-develop-their-public-speaking-skills/?sh=62ba80f5200e


Personal Reflection
My nursing journey has been filled with growth, reflection, and transformation. Initially, I dreamed of becoming a veterinarian, but after facing repeated rejections, I felt disheartened and uncertain about my future. However, I eventually realized I needed to take control and started researching career options. This led me to nursing, a profession that combined my love for science with my desire to care for others. With encouragement and insight from my mother, a nurse, and my sister, a nurse practitioner, I applied to Trent’s nursing program and was accepted, marking a significant milestone in my journey.
Before pursuing the program, I worked in the veterinary field for over five years, where I gained valuable experience in animal care. As a veterinary assistant, I was responsible for ensuring the well-being of patients, which has been crucial in shaping my approach to nursing. Compassionate care is key in both fields, and my veterinary background provides me with a unique perspective, particularly in understanding the emotional and psychological aspects of patient care. That compassion has the power and influence to guide how one makes decisions through self-reflection and prioritization of needs to ensure optimal outcomes (Raustøl & Tveit 2023).
While I am new to nursing, I am not entirely new to the themes of care and assessment that I first encountered in veterinary practice. I now find myself in what I would call a “post-novice”, or advanced beginner stage—strengthening one’s understanding of new theory behind clinical practice and learning how to apply it in real-life situations (Ozdemir, 2019). Studying nursing requires a lot of strength and dedication; it’s about developing critical thinking skills and learning how to apply them to nursing care (Ozdemir, 2019). I’m beginning to gain confidence in making informed clinical judgments, however, I recognize that I still have a long way to go before reaching a stage of mastery (Ozdemir, 2019).
One of the biggest challenges has been adjusting to the academic workload after several years away from school. But more importantly, I recognize that nursing students must also learn how to manage stress and avoid burnout. The healthcare field is demanding, and maintaining balance through mindfulness and self-care is essential to long-term success (Aryankhesal et al., 2019; Dall’Ora et al., 2020). I’ve started incorporating these practices into my routine to ensure I remain focused and healthy (Dall’Ora et al., 2020).
An unexpected benefit of nursing school has been the sense of community it fosters. Despite busy schedules, the support and friendliness of my classmates are motivating, reminding me that we share the same goal of becoming skilled, compassionate nurses. My coursework in NURS 1001 has also deepened my understanding of nursing practice, particularly the importance of ethical patient-centred care, where the patient is an active participant in their own healthcare decisions. This focus on holistic care—caring for the whole person rather than just addressing their medical needs—has solidified my passion for the profession.
Reflecting on this transition from veterinary care to nursing, I am excited about the journey ahead. The challenges I’ve faced in the past have been opportunities for improvement, and I am learning and refining the skills I need to succeed both in my clinical placements and in my future as a nurse. I am genuinely excited about what lies ahead and confident in the knowledge and experiences I’ve gained so far. As I continue my studies, I maintain a positive outlook and a deep commitment to making a meaningful difference in the lives of others.


Applying Basic Marketing Principles
Social Media
Some people are confused about social media, but it’s essential to understand that social marketing has been around for a long time. Digital and social media marketing are not new philosophies; they are traditional practices adapted to new tools. Historically, business was conducted in social settings like door-to-door sales or marketplaces. These gatherings allowed people to share ideas and communicate across networks. Similarly, event marketing created connections between buyers and sellers through dealer conferences or even extravagant parties attended by influential individuals.
Nowadays, many of these connections happen online through platforms like LinkedIn or Facebook. However, some businesspeople shy away from using these modern technologies as they appear daunting compared to traditional methods such as television, radio, newspaper advertising or direct mail campaigns. The ease of digital marketing allows businesses to quickly share their stories by taking pictures or conducting interviews with just a smartphone. Despite the low cost of entry into this form of promotion, many entrepreneurs still find it challenging due to lack of education in marketing principles and strategy creation.
Social media is simply another way to market a product or service using traditional theories adapted for new mediums. Each platform has its own language and style which requires tailored communication strategies for success. The main difference between traditional and modern-day digital/social media marketing lies in the technology available today rather than any significant change in underlying principles.
Before we move forward, let’s go back to some of our earlier definitions of marketing by Seth Godin;
“Marketing is at the core of what we do. It is the story you tell, who you’re telling it to, and why people are going to buy your product or service.”
“Marketing is no longer about the stuff that you make, but about the stories you tell”.
Translating Marketing Mix to Social Media
The 4Ps Re-imagined. While social media marketing is relatively recent in the grand scheme of things, marketing itself isn’t new at all. Applying foundational marketing concepts to social media is not just essential, but also incredibly effective. By grounding your social media strategy in these tried-and-true marketing principles, you’ll be better equipped to leverage these platforms and communicate your brand message powerfully and persuasively.
- Product (product or service). It’s critical to understand what sets your product apart and how it enriches your customer’s life. These unique insights allow you to effectively utilize platforms like LinkedIn, Instagram, or YouTube to tell your product story. Keep in mind that savvy customers today are not just buying a product; they’re investing in your brand’s narrative, which can include your connection to community, your social and environmental responsibility, and or your family connection to the product.
- Price. This isn’t just about the dollar value; it’s about the perceived value your product delivers. Striking the right balance in pricing is paramount. You don’t want to scare off customers by being too expensive, nor do you want to sell yourself short. E-commerce and social media have changed the pricing landscape, allowing you to operate with leaner margins and potentially pass the savings onto your customers. Techniques such as Dropshipping and Just-In-Time manufacturing can be powerful tools in your arsenal to manage costs.
- Place. This term encapsulates all the platforms where customers can find or access your offerings. Social media has revolutionized this aspect, making it possible for customers to shop from their living room while allowing you to engage, respond, and improve the customer experience in real-time.
- Promotion. Traditional marketing techniques still have their place, but the digital landscape, especially social media, has opened up new possibilities. You can foster lasting relationships with your customers, earn their trust, and transform them into advocates for your brand. Promoting your brand on social media, optimizing your website for search engines, and leveraging email marketing can be cost-effective ways to enhance your visibility and reach.
As you craft your social media strategy, keep these principles at the forefront. Each one provides a lens to view your product, your customers, and the market. They aren’t mere steps, but ongoing considerations that can help your brand connect, engage, and grow in the dynamic world of social media.


Emotion and Motivation
Introduction to Emotion
What you’ll learn to do: explain theories of emotion and how we express and recognize emotion
As we move through our daily lives, we experience a variety of emotions (which we often call “feelings”). Emotions are subjective states of being that, physiologically speaking, involve physiological arousal, psychological appraisal and cognitive processes, subjective experiences, and expressive behavior. Emotions are often the driving force behind motivation (whether positive or negative) and are expressed and communicated through a wide range of behaviors, such as tone of voice and body language.
Our psychological appraisal of a situation is informed by our experiences, background, and culture. Therefore, different people may have different emotional experiences of similar situations. However, the ability to produce and recognize emotional facial expressions seems to be universal. That said, cultures differ in how often and under what circumstances it is “okay” to express various emotions, as well as how various expressions of emotions are interpreted.
Learning Objectives
- Compare and contrast the the Cannon-Bard, James-Lange, Schachter-Singer two-factor, and other theories of emotion
- Describe the role that limbic structures play in emotional processing
- Classify and explain how emotions are recognized and expressed
Licenses and Attributions (Click to expand)
CC licensed content, Original
- Modification, adaptation, and original content. Provided by: Lumen Learning. License: CC BY-SA: Attribution-ShareAlike
CC licensed content, Shared previously
- Describing Emotion. Provided by: Boundless. Located at: https://www.boundless.com/psychology/textbooks/boundless-psychology-textbook/emotion-13/defining-emotion-503/defining-emotion-504-16761/. License: CC BY-SA: Attribution-ShareAlike
- Emotion. Authored by: OpenStax College. Located at: https://openstax.org/books/psychology-2e/pages/10-4-emotion. License: CC BY: Attribution. License Terms: Download for free at https://openstax.org/books/psychology-2e/pages/1-introduction
- Portrait of a Man showing emotions. Authored by: Gert Germeraad. Located at: https://commons.wikimedia.org/wiki/File:Portret_van_een_man005.jpg. License: CC BY-SA: Attribution-ShareAlike


32 From the Field: The Perfect Pitch
Amy Eisman
How to avoid the dreaded blank stare during a live presentation. ‘Good ideas die all the time,’ one expert reminds us.
From the Field
What makes a compelling, memorable presentation? What will make investors sit up and take notice?
Most experts say the first thing a startup presenter should do is tell a good story. You have to be engaging, even entertaining, explains Tom Davidson, former senior director of PBS Digital, now in product development at Gannett.
Executive coach and author Peggy Klaus calls that “painting images about how this product or company could impact the audience.”
Klaus, president of Klaus & Associates, has seen thousands of presentations — from executives and entrepreneurs, to private bankers and nonprofits. She tells clients to keep the audience in mind by embracing fictional radio station WIFT-FM — where the call letters stand for what’s in it for them?
“Most people who start a speech or presentation think about what I want to say, what is my point,” Klaus says. “That is a narcissistic way of looking at it. What are their goals and objectives?”
Insiders admit the soul of a good pitch presentation is really common sense. Don’t dare read your slides. Be confident and concise. And of course practice, practice, practice.
“People think they can wing it because they’ve been verbal since 18 months,” Klaus says. “This results in a terrible meltdown situation.”
Below, the experts weigh in on the perfect pitch:
Your parents were right.
“Maintain eye contact with your audience,” says Jan Schaffer, who has funded 220 media entrepreneurship and innovation projects as Executive Director of J-Lab: The Institute for Interactive Journalism. “Walk around. Be at ease. Show some personality without being obnoxious.”
They were right about this, too.
Introduce yourself, says Schaffer, who teaches media entrepreneurship at American University and the CUNY Graduate School of Journalism.  Your audience won’t always be classmates.
Be armed.
Have one or two sentences that show that you, as the founder, have a firm grasp of the opportunity, says Ju-Don Marshall Roberts, startup advisor and coach and now Chief Content Officer for WFAE.FM. Convey enough passion to show you are the one to pull this off.
Davidson emphasizes that you simply can’t let the investors, humans like the rest of us, get distracted. If you don’t know an answer, tell them an exact time you will get back to them with the response.
Define your opportunity.
Will the market sustain the product? Have you explained how your idea is different from a similar one? “Good ideas die all the time,” Roberts says.
Equally critical: Convince funders that this is a business, not a hobby, Schaffer says.
Bring a solid team.
“I’ve seen a lot of pitches where you think, ‘This is a great idea, I wish someone else was doing it,’” Roberts says.
Memorize your pitch and don’t read your deck.
“Likewise, don’t read from your laptop or cell phone,” Schaffer says.
Klaus has seen so many presentations that a question about biggest mistakes momentarily stumped her. “There are so many. Where do I begin?”
She identifies some of the top presentation mistakes as using jargon, causing death by PowerPoint, speaking longer than seven minutes before interacting with the audience, and being condescending or arrogant.
Klaus also warns against promising future results and cautions that conditional language is preferred. “With our numbers, we see a future where we can … “
Klaus warns that young people’s nerves often get the best of them. They end up talking quickly or speaking with an upward inflection (making statements sound like questions). They fidget. They twist their hair. They slap their thighs.
Klaus says young presenters have a particular challenge that interferes with the enthusiasm our experts say is critical. “A lot of young people feel if they show passion and excitement they will come off as too exuberant or too young,” says the author of Brag! The Art of Tooting Your Own Horn Without Blowing It. “It is actually the inverse — that young people feel, ‘If I am really serious, they will think I am really smart.'”
In the end, make a video of yourself while practicing your pitch. Yes, we know you hate seeing yourself perform.
For examples and pitching resources, see this chapter.[1]
Amy Eisman is director of media entrepreneurship at the School of Communication at American University in Washington, D.C. An innovator in journalism education and consultant, she held previous editing positions at AOL, USA Today, USA Weekend, and others. She is a former Fulbright lecturer and chairs the MJ Bear Fellowship Committee for ONA. Reach her on Twitter at @aeisman.
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- CJ Cornell, "Startup Funding: Why Funding," Media Innovation and Entrepreneurship, https://press.rebus.community/media-innovation-and-entrepreneurship/chapter/section-2-why-funding/. ↵


Introduction to Harriet Ann Jacobs by Wendy Kurant
Harriet Ann Jacobs (c. 1813–1897)
by Wendy Kurant
Harriet Jacobs was born into slavery in Edenton, North Carolina, around 1813. Her father was probably a skilled carpenter allowed by his master to hire himself out. Though he and Jacobs’ mother were owned by different masters, they were allowed to live as a couple with their children. Jacobs’ maternal grandmother, Molly Horniblow, was a freed slave who owned a house in Edenton. After her mother died, Jacobs lived as slave in the household of Margaret Horniblow, who taught Jacobs to read. Upon Margaret Horniblow’s
death, Jacobs was willed to the daughter of Dr. James Norcom and brought into his household.  His wife, out of jealousy, subjected Jacobs to physical abuse.
Jacobs defied Norcom by taking Samuel Tredwell Sawyer, a white lawyer, as her lover. She had two children, a boy and a girl. As punishment for Jacobs’s prolonged defiance, Norcom sent her out to work on his plantation, where he also threatened to send her children. She ran away and hid from Norcom for almost seven years in her maternal grandmother’s attic. Sawyer bought their children but did not free them (as Jacobs wrote that he had promised to do).
In 1842, Jacobs escaped to the North, later followed there by her children. She gave domestic service to writer and editor Nathaniel Parker Willis (Fanny Fern’s brother). Willis’s second wife would buy and emancipate Jacobs in 1852. Before that freedom, Jacobs was vulnerable to being captured and returned to Norcom. To avoid this danger, she went to Rochester, New York, where her brother John S. Jacobs (1815–1875) was also a fugitive slave who worked for abolition.
Starting in 1849, she worked for the American Anti-Slavery Society office located in the same building as The North Star, the anti-slavery newspaper founded by Frederick Douglass. Jacobs took full advantage of the literature available where she worked. She also became friends with Amy Post, a Quaker reformer, who encouraged Jacobs to contribute to anti-slavery literature by writing her own story. After five years, Jacobs completed Incidents in the Life of a Slave Girl in 1858. Aware of the cult of domesticity and sentimental literature—as exemplified by Stowe’s Uncle Tom’s Cabin—Jacobs’ story emphasized how slavery betrayed the highest ideals of womanhood and woman’s purity, not only the womanhood of female slaves but also of slave mistresses. She described the peculiar horrors of her situation, in being forced to give herself sexually to one man to avoid being sexually abused by another, and in having her children bought by their white father to help them escape their legal master. Lydia Marie Child wrote the book’s preface and helped Jacobs have it published in Boston under the pseudonym of Linda Brent. It sold well until its message seemed to be obviated by the Civil War, but it gained renewed attention in the 1980s.
Source:
Becoming America, Wendy Kurant, ed., CC-BY-SA
Image Credit: Photograph of Harriet Ann Jacobs, Public Domain, Wikimedia Commona


Chapter 1 – Introduction to Fitness for Paramedics
PARA Fitness Test Standards
Fitness Test Weight
The weight of each test (i.e., how much each test counts towards your final grade) will vary based on your current semester/course code in the Paramedic program. The table below indicates the weight of each test for each Paramedic Fitness course. Note – for Semester 3 PAR 1301, all three Fitness Tests must be successfully completed to pass the course, regardless of the attributed weight.
| Test / Semester | Semester 1 – FIT 1101 | Semester 2 – FIT 1201 | Semester 3 – PAR 1301 |
|---|---|---|---|
| PET | 10 % | 10% | 10.5% |
| Shuttle Run | 10% | 10% | 10.5% |
| Stair Chair / Stretcher Carry | 40% | 40% | 31% |
Fitness Test Performance Goals
The Paramedic Fitness courses are designed to build upon one another, beginning with the lowest performance goals in Semester 1 and the highest performance goals (equivalent to the City of Greater Sudbury’s Emergency Services fitness standards) in Semester 3. This allows students to gradually develop their fitness throughout their time in the program so they may succeed during preceptorship and upon graduation. With this in mind, the Time and Stage standards (and attributable grades) become harder for the PET Test and Shuttle Run, respectively, while the weight of the manikin increases significantly for the Stairchair and Stretcher Carry. You will find a detailed breakdown of the Performance Goals for the PET and Shuttle Run in the tables below:
PET Standards and Grades
| MALES | 1101 Grade | 1201 Grade | 1301 Grade |
|---|---|---|---|
| =< 2:35 | 100 | 100 | 100 |
| 2:36 – 2:40 | 95 | 95 | 95 |
| 2:41 – 2:45 | 92 | 92 | 92 |
| 2:46 – 2:49 | 90 | 90 | 90 |
| 2:50 – 2:54 | 88 | 88 | 88 |
| 2:55 – 2:59 | 85 | 85 | 85 |
| 3:00 – 3:04 | 82 | 82 | 82 |
| 3:05 – 3:09 | 80 | 80 | 80 |
| 3:10 – 3:14 | 78 | 78 | 78 |
| 3:15 – 3:19 | 75 | 75 | 75 |
| 3:20 – 3:25 | 72 | 72 | 72 |
| 3:26 – 3:30 | 70 | 70 | 70 |
| 3:31 – 3:45 | 60 | 0 | 0 |
| =>3:46 | 0 | 0 | 0 |
| FEMALES | 1101 Grade | 1201 Grade | 1301 Grade |
|---|---|---|---|
| =< 2:50 | 100 | 100 | 100 |
| 2:50 – 2:54 | 95 | 95 | 95 |
| 2:55 – 2:59 | 92 | 92 | 92 |
| 3:00 – 3:04 | 90 | 90 | 90 |
| 3:05 – 3:09 | 85 | 85 | 85 |
| 3:10 – 3:14 | 82 | 82 | 82 |
| 3:15 – 3:19 | 80 | 80 | 80 |
| 3:20 – 3:25 | 75 | 75 | 75 |
| 3:26 – 3:30 | 70 | 70 | 70 |
| 3:31 – 3:45 | 60 | 0 | 0 |
| =>3:46 | 0 | 0 | 0 |
Shuttle Standards and Grades
| MALES | 1101 Grade | 1201 Grade | 1301 Grade |
|---|---|---|---|
| 10 | 100 | 100 | 100 |
| 9.5 | 95 | 95 | 95 |
| 9 | 90 | 90 | 90 |
| 8.5 | 85 | 85 | 85 |
| 8 | 80 | 80 | 80 |
| 7.5 | 78 | 78 | 78 |
| 7 | 75 | 75 | 75 |
| 6.5 | 70 | 70 | 70 |
| 6 | 65 | 65 | 0 |
| 5.5 | 62.5 | 0 | 0 |
| 5 | 60 | 0 | 0 |
| <5 | 0 | 0 | 0 |
| FEMALES | 1101 Grade | 1201 Grade | 1301 Grade |
|---|---|---|---|
| 8 | 100 | 100 | 100 |
| 7.5 | 90 | 90 | 90 |
| 7 | 80 | 80 | 80 |
| 6.5 | 70 | 70 | 70 |
| 6 | 65 | 65 | 0 |
| 5.5 | 62.5 | 0 | 0 |
| 5 | 60 | 0 | 0 |
| <5 | 0 | 0 |
Stair Chair and Stretcher Carry
Stairchair and Stretcher Carry Manikin Weight Increments
The manikin weight will increase per semester/fitness course as follows:
- Semester 1 – FIT 1101: 70kg (154 lbs)
- Semester 2 – FIT 1201: 80kg (176 lbs)
- Semester 3 – PAR 1301: 90kg (209 lbs)
Beyond the need to avoid Unsafe Critical Errors, which would lead to test termination during the Stairchair and Stretcher Carry, performance will be assessed using the marking rubric below. As made evident by the rubric, marks are emphasized for proper technique and patient safety.
| Unsafe 0% | Marginal 70% | Competent 80% | Highly Competent 90% | Exceptional 100% |
|---|---|---|---|---|
|
|
|
|
|
Chapter attribution to Fitness for Paramedics, 1st ed. by Martin Dubuc. Standard and Grade Charts can be found in their original image form at Fitness for Paramedics, 1st ed.