• Define torque
  • Define static equilibrium
  • Determine the resultant of two or more torques
  • Determine if an object is in static equilibrium when the forces and torques acting on the object are known
  • Determine an unknown force or torque acting on an object, if all the other forces and torques acting on the object are known and the object is in static equilibrium
  • Define center of gravity
  • Estimate the location of the center of gravity of an object or body

Torque: The turning effect produced by a force

Book example

Ruler example

Lever systems

Inside the body (Whole-body reference, Single-joint reference)

Mechanical advantage:
Resistance Force/Effort Force
or Effort Arm/Resistance Arm

Tools provide an excellent example of using torques

Torques in diving

Wrestlers use torques to reposition their opponents

Are there torques in Miles Batty's race?

Curve Running

Muscle forces and torques

What is the purpose of a patella?

How much does a patella matter?

Muscle force knee extensors


Baxter JR, Novack TA, Van Werkhoven H, Pennell DR, Piazza SJ. Ankle joint mechanics and foot proportions differ between human sprinters and non-sprinters, Proc Biol Sci. 2012 May 22;279(1735):2018-24

"We found that trained sprinters have shorter plantarflexor moment arms (p = 0.011) and longer forefoot bones (p = 0.019) than non-sprinters."


Equilibrium: Forces and Torques Must Balance

What happens as the angle of force changes?

Sample problem

Is there a benefit to having the joint position that maximizes the effort arm being a different position than the joint position that maximizes muscle force?

Where is our center of mass?
Center of mass in a gymnast

How can we use these principles in sport?
Side Leap

Stability: The capacity of an object to return to equilibrium or to its original position after being displaced

Factors affecting stability:

  • Height of the center of mass
  • Size of base of support
  • Weight of object

How do we calculate center of mass position?

Body segment parameters

Calculating center of mass in a body
The shoulder of a tennis player is 1.60m above the ground while the elbow is 1.77m above the ground. Where is the center of mass of the upper arm (the length percent for the upper arm is 43.6%)?


Emma Coburn jumps off the steeplechase barrier with her right leg in the following position from a side view in meters relative to the ground vertically and from the front edge of the barrier horizontally:
Hip (0.84, 1.44)
Knee (0.65, 1.12)
Ankle (0.31, 0.92)
Heel (0.29, 0.95)
Toe (0.25, 0.72)
Where is the center of mass of the leg if the body segment parameters are as follows:

Segment Length Percent Mass (kg)
Thigh 43.3 7.05
Shank 43.4 3.21
Foot 50.0 0.80


High jump example of center of mass