It has to be kind of a rough summary of the entire unit. I will try, OK? Some key ideas. When we talk about, you know what? I'm not going to try and tell you. I just have to live with my messy handwriting. When we talk about circular force, it's mass times circular acceleration. There is, I don't know if you noticed, there's no circular force equation on your formula sheet. What there is is two equations for centripetal or circular acceleration. Either of those gives you the same answer. I would use this one if they gave me the speed or asked me for the speed. I would use this one if I knew the period or they wanted me to find the period. Some key ideas. We said the direction. So if you're moving in a circle, let's try drawing a circle, Mr. Dewick. That's no good. Let's try drawing a circle, Mr. Dewick. Is that a circle for you guys? On my screen, it's not, but the projector distorts everything. So if you're moving in a circle, there's three directions. Let's say, let's put the object right here. And let's pretend you're moving in this direction around a circle. Something is spinning, let's say. What direction is the velocity in A, B, or C? Desmond, can you contact Mr. Nixon, please, in the office? Desmond, contact Mr. Nixon? A. Fancy word, tangent to radius. What direction is the acceleration in? A, B, or C? B. What direction is the force in? A, B, or C? Because force is mass times acceleration, they've got to have the same vector. And the fancy word for this was centripetal. And the phrase that we used was we said it was center seeking. By the way, let's suppose there was a string right here. If I cut the string, which way would the object move off? Direction A or B or C? A, same direction as the velocity. Because as soon as I cut the string, that inwards force is gone, so now it's going to move Newton's first straight law, straight line constant speed. I don't think this is on your formula sheet. Is circular velocity on your formula sheet? You have it right there, Pat, can you check? We said that in case you ever need to figure out the velocity when you're moving in a circle, this shows up once in a while, we said this. Velocity is distance over time, assuming you're going at a steady speed. And when you're moving in a circle at a steady speed, your acceleration is inwards, but your speed is not changing. So this does work. What's the distance around a circle? We call it the circumference. What's the equation for the circumference? And what variable have we used when we go around once? Period. The circular velocity, if they ever ask you how fast is an object traveling in a circle, it's 2 pi r times the time that I divided by the period. That's distance over time, it's meters per second. That's the tangent to radius velocity. The last key idea that we said, FC is net force. It never appears body, Mr. Deweyke, diagram.  It never appears on a free body diagram. That's what I mean when I said it never appears on a free body diagram. I'm going to do some examples, can you hang on? But it's never going to appear ever. You'll never see me draw FC on a diagram. Ever. Ready? Let's look at some examples. The first thing we looked at was horizontal circles. I'll type just that once. Nope, too far. Can you bear with me while I find the horizontal circle or two? So here's one right here. Athlete runs at a constant speed around a circle of radius 5 in 12 seconds. What are the athletes speed and acceleration? OK. Let's do acceleration first. Acceleration is v squared over r. Do I know how fast this athlete is traveling? Do I know how fast this athlete is traveling? Nope. By the way, this is number two from the review. I'll pick some from the review if you want to. You can follow along or you can just watch. So I'll use the other circular acceleration. What's the other circular acceleration equation? 4 pi squared r over t squared. Do I know the radius? Yep. Do I know the period? Yep. Good. It's going to be 4 pi squared times 5 over 12 squared. What's his circular acceleration? Someone crunch that for me, please? I get 1.4 meters per second squared. So I would right away do that. Yes, no. Yes, I already know the answer is b or d. Now we need to find his speed. There's two ways we could do this. We could find his speed from there. 1.37 equals v squared over 5 times by 5 square root. And I might do that since I have it on my calculator already. I'm going to go times by 5 square root. I get 2.6. Or the other way, remember we said velocity is 2 pi r over the period. It's circumference over time. That'll also work if I put the data back up there. 2 times pi times 5 divided by 12. And I also get 2.6179999. Correct answer, d. Now that wasn't actually doing any free body stuff. Let's find a horizontal circle. We've got to do some free body stuff. I know of a few questions I'm thinking about there. I'm going to go view, page display, single page continuous though. That's vertical, that's vertical, that's vertical. A car travels 25 meters per second along a horizontal curve of radius 450. What's the minimum coefficient or friction necessary between its tires and the road in order for the car not to skid? So I'm going to do a picture. Here's the car looking right at us. So there's the front. There's the headlights. There's the roof. There's the tires. He's coming right towards us. And he's going around a circle in that direction there. So here's the road. Is that OK? That's my high tech, very artistic free body diagram as good as you're going to get. What are the forces acting on this car? Get the obvious one. MG down. Is the car falling into the pavement? Then there must be a normal force pushing it up. How is this car moving? What path is it tracing out? A circle. Where must the net force be towards the center? There has to be a force that way, but it is not going to appear on my diagram as FC. I need to figure out what force that there is. What force is pushing this car in a circle? But do you see an FC anywhere in my diagram? That's what I was getting at. Horizontally, winner, no loser, equals FC, because we're moving in a circle. Friction is what times what? I don't know the normal force. Let's see here. UMG equals M. I don't forget the M. Do I want to use the one with the period in it, or do I want to use the one with the speed in it? What if they give me this question for acceleration? Sorry. Now I started to panic for a second there. It hesitated because I was going, they didn't tell me the mass of the car. Wait a minute. They didn't need to tell me the mass of the car. That's why semi-trucks can drive next to little VW bugs. It looks like mu is going to be D squared over G. Can I assume that you can crunch the numbers on your own and get the right answer? I don't know what the answer is, but you have the rest of it on there. Is that all right? That way we'll get through more examples. So there's a good example of a horizontal question. Let's do an ask to your one. I know which one I'm looking for. I'll recognize it when I see it. There was a table with something hanging underneath the table. I recall. Oh, I like this one actually too. This is a horizontal circle. Number 18, I believe this is. So what we have here is what we call the conical pendulum. Yes. Is that a horizontal circle? Yep. I know the strength of that. Who cares? The circle is horizontal. What are the forces acting on this mask at the obvious ones? Pardon me? I never put circular force on my diagram. If you can't tell me the name of that force, don't be putting it on there. Tension, absolutely. Like the tension in this room when I just glared at you because I didn't mean to be that hard at you by the way. Those are the only two forces. Watch what happens when I add these together vectorially. How do I add them together vectorially? Add them. Mg plus tension. I know I have to stop right there, Pat. I know I can't go further. I know I can't go shallower because what did you tell me my net force has to be Pat? This is what you were trying to spot. It doesn't appear on the free body diagram. You were saying, well, I know my overall force has to be pointing in which direction. It shows up not on my free body diagram, but on my vector triangle, in this case, for the conical pendulum. Ooh, and it's even going to be Selkatoa. Oh, and they don't even want me to find the acceleration or velocity or period. They just want me to find the force, although if I found FC, could I find V or period? Yes, and we'll talk about that in just a second. Let's see. Do I know the mass? OK, great. Then I can go like this. Oh, that's 39 degrees. So tension next to a vertical line is 39 degrees. Tension next to a vertical line is 39 degrees. See the z? I think that's 39 degrees down there, too. Which trig function relates these to? Tangent of 39 equals opposite over adjacent. FC equals mg tan 39. I'm going to add a part B to this question, because I think another nice extension, given all this information, might be to say part B, find the speed. What's another way to write FC that might have a speed in it? That's an acceleration. Don't forget what you have to put in front of it, please. What if put in front of it? You're giving me an acceleration. No, no, no, even simpler than that. No, no, even. Forces what times what? You're not giving me the mass. You're telling the only acceleration. You're doing this. And that's totally wrong, because you know what's going to happen to those masses, Jafar. You're going to cancel. Don't forget that's not a force on your formula sheet. It's an acceleration on your formula sheet.  By the way, am I harping on a common error that drives me crazy? Yes. Let's see. Did they give you the radius? So could you find the velocity? Would that be a fair question? I think so. Or as a part c, instead of finding the velocity, I could ask you to find the period. Same diagram, same information. I would go m for pi squared r over t squared equals mg1039. By the way, up here, let's finish this. I think v would be the square root of rg1039. And I'd go type that in, so you can do that, right? Here, once again, the masses would cancel. Here, I think the period is going to be, let's see. It would move up here. Those would move down. It's going to be 4 pi squared r all over g1039 square root. Yes, I hope I think. That's all hidden in there, too, in the conical pendulum. Let's go back here. What haven't I used yet, that 1.9? Why'd they give it to me? Throw y'all. Well, no, what they wanted to do is they wanted to give you at least one different thing in meters to tempt you to make a sloppy mistake. Instead of the radius, pick the length of the string. So all of that can be contained in that one little question there. Am I right? 4 pi squared r over g1039 square root, right? Yeah. OK. Oh, if you knew the velocity, could you figure out the mass? Maybe. Certainly, if you knew the tension. So another twist, instead of giving you mg, if I didn't give you the mass, but I told you the tension in the cable, you could use this. Except here, I think you'd be using sine or coast or whatever. So don't just lock yourself into tangent. But this conical pendulum, I can do a lot with that as a horizontal circle. Last one, I know what I'm looking for. I know what I want to see it. Show me the table. Maybe 21. I thought there was a yuckier one. Serious, Mr. Duke? You had one on here. Maybe it was in the homework. Let's go do 21 there. I think I said it was 21, right? Let's go find 21. Find the next one. Find this one. There we go. That's what I was trying to get to. Stop there. Stop there. Don't do that. OK, fine. Here's a good example. Horizontal circle again. Oh, in this case, they want me to find the maximum mass. So they're saying this rope can withstand the maximum tension of 6.3 newtons. Going to make it, Mr? You sure? OK. If it goes faster and faster and faster, the tension would go bigger and bigger and bigger. But if it spins at a certain speed with a period of 2.1, what's the biggest mass we can put on there before the stringles now? OK. What are the forces acting on this guy? Get the obvious ones. Gravity down, normal up. How is this moving in a circle? Where must my net force be towards the middle? So there has to be a force here. What? Tension. Tension equals fc. Tension equals jafar. Don't forget the m. And then do I want to use the equation that has velocity or period in it? What do they want me to find in this question? The mass. I got a bit of a problem here. What letter did I use for period? What letter did I use for tension? So you know what? I'm going to do this. I'm going to call it force in the rope. Otherwise, I'm just going to get confused, aren't I? I started to pull a t cubed out of there and go, wait a minute. That's not going to happen. Anyways, the mass is going to be the force on the rope times the period squared divided by 4i squared r. Do I know the radius? Oh yeah, they gave it to me in the diagram. Do I know the period? 2.1 seconds. Do I know the force? 6.3 newtons? Yeah, I can find the mass. Yeah.  That moves up. Those move to the bottom. That moves to the top. Well, again, what is on your formula sheet? Acceleration. So if you want a force, force is what times what? You better have that. So yeah, that doesn't appear. Look at a couple of vertical circles. Vertical, vertical. There's two main types of vertical circles. The first is the airplane doing a loop. Because in an airplane doing the loop, your head points down. So here would be an example. A pilot of mass, 65 kilograms, is in an airplane traveling at how fast do planes go? Well, in miles per hour, let's say, let's make it a bit of a jet. Let's go about 400 miles per hour. So let's say about 220 meters per second. The pilot enters a loop of radius 1,100 meters. Find the normal force at the bottom of the loop. I'm not going to try drawing a picture if that's OK. I'm hoping you guys can visualize it. At the bottom of the loop, here's our pilot. What are the forces acting on him at the bottom? Oh, sorry, you guys are still writing. Yeah, I'll get the thing, if people are still writing this. You know what, Tandon? I'll just clean it. Done? Good. What are the forces acting at the bottom? Jimmy, I agree. MG, what else? Why did I draw it bigger? Because at the bottom, the center of the circle is upwards, and he's moving in a circle. Where must the net force be pointing towards the middle? Which force is pointing towards the middle? Normal force. It's got to be the winner, destiny, destiny. So my equation is going to look like this.  Again, Jafar, did FC appear anywhere on the diagram? No. It appears on the right-hand side. It's my net force.  The normal force is going to be plus the MG over, plus. FC is going to be, don't forget the M. Am I going to use V squared over R or 4 pi squared R over T squared? I've heard two answer. Which one? Y. Yeah, didn't give you the period. Hey, crunch the numbers, see what you get. 65 times 9.8 plus 65 times 220 squared divided by 1,100. I may have made up terrible numbers. It's possible this pilot might die. That's why I want to know. And you guys are laughing at that? You guys have seen way too many movies.  Do you always get 3,500? I get a normal force of 3,000. Well, I guess if I go to three-sig figs, it's 3.5 times 10 to the third newton. I just want to divide that by 9.8. How many G's is he getting? Yeah. 350 G's. T's more than that. G would be 9.5 to the power of 5.5. Yep. Only 220 squared. Well, I'll apologize and I'll simply say dead pilot. But let's do B. Let's find the normal force at the top. Now at the top, you need to realize if you're in a plane, there's your legs, there's your body. Your head is pointing downwards. So what are the forces acting on this pilot? Get the obvious one. Mg down. Which way is the normal force acting? Down.  Mg plus normal force equals Mv squared over R. Equals FC, but I've plugged in the equation already. At the top, the normal force is going to be Mv squared over R. Take away Mg. Conveniently, I have Mg plus Mv squared over R on my calculator. So I'm just going to make the Mg the negative in front. Mr. Goulet, could you please call extension to 00 please? Immediately? OK, I get. Still dead, but you do feel a little bit lighter at the top of the loop if you're on the inside. Now, I called this the airplane. On a roller coaster, are you on the inside of a loop or the outside of a loop?  Top of a loop, your head's pointing down on a roller coaster. No, no, no, no. Roller coaster doing a loop here. Top of a loop, your head's pointing down. That's a lot. What about a ferrous wheel? OK, so this gives us the second type of question. Ferrous wheel type. I think I have one of those in here. So let's, ah, look at that. Number 22 was a vertical loop that probably wouldn't have killed him. Oh well. I know I have a ferrous wheel picture in here somewhere. 41. I know 16 is as well, but I kept the moon forward. Can I get this on a little page? Pretty close. 75 kilogram person rides the ferrous wheel, which is rotating. And it tells me the centripetal force in this case. It says 45 newtons. OK, a little twist. Instead of finding FC, they're telling me FC, and they want me to find what force the seat exerts on the top or the bottom. Now instead of telling me FC, remember they could have given me the velocity and the radius, and I could figure out FC. Or they could have given me the radius and the period, and I could have figured out FC. In this case, they gave it to me. That's fine. At the top, what are the forces acting on this person? Get the obvious one. Gravity, which way down? Which way is the normal force here? Why do I draw it smaller? Because I know the net force has to be towards the middle because it's moving in a circle. At the top, I have mg minus fn equals 45. I have the normal force equals mg minus 45. I'm going to show you, by the way, we don't even actually need to crunch the numbers for this one. We can figure it out by being clever. Bottom, mg, why don't I draw the normal force bigger because it's moving in a circle and that force has to be towards the middle? Normal force minus mg equals 45. At the bottom, the normal force equals 45 plus mg. Don't get a calculator. Bottom's going to be more because you're adding. Top's got to be less. It's got to be that one. By the way, I would have said that one's wrong. It's not the same in both. I've been on Ferris wheels. If you're lighter at the top, dude, those are vertical circles. Yeah. But I'm a nerd. I think differently for most of you guys. Then we brought in gravity point.  Be prepared, though, for me to do something like this. Instead of saying calculate the force, what if I give you the force and say, find the mass of the planet? You guys handle that, OK? In other words, so we moved on to gravity. If I tell you that and the radius and the satellite, can you tell me the mass of the planet? Can you solve for that? I hope so. Or if I tell you the mass of the planet, how big the satellite is and what force it's experiencing, could you tell me how far it was from the center of the planet? Then we also added gravitational field strength, which I did a big song and dance about today. I said that was that there, OK? So if they mentioned gravitational field strength and you only see the mass of the planet, don't freak out. Or if I tell you the gravitational field strength and how high we are, could you then figure out the mass of the planet? Or if I tell you the gravitational field strength and I tell you what planet we're on, by the way, don't expect that you're on Earth on the test because an easy way to change a question is to put you on the moon or around the sun or around the planet, ubernerd or whatever I want to and make it my own stuff. Could you tell me how high you are? OK. But what you guys are really wondering about is something like this. So I want this combined gravity circular questions. Let's make a new planet, mass. Let's suppose we have a planet A, J, B, P. No, wait a minute. J, if your last name for some reason. JJPBX has a mass of 6.36 times 10 to the 30, a little bit bigger than Earth, has a radius of 7.2 times 10 to the 6 kilograms in meters. So there's our mystery planet. What can I ask you? Number one, satellite is in orbit. It goes around the planet once every 16 hours. It is its orbital radius, speed, its orbital velocity. When they start asking you, when they start talking about something in orbit and they're talking about orbital radius or period or speed, what we're really saying is that you're moving in a circle and the force that's pulling you in a circle is gravity. What we're really saying is this.  FC depends. Don't forget to write the M. If anybody knows where the Mexican students are at this moment, could you please contact 203 regarding Mexican students that are here in the building, please, 203? Did they give me the speed in this question? The period, except the period in what? Can you tell me how many seconds that is, please? Yeah, you have to go time 60, time 60. Can you do it? Sorry? 16 times 60 times 60. So I'm going to use the 4 pi squared R over T squared. Now, the nice thing is, what do you notice about the little masses? Because I didn't tell you how heavy the satellite was. What are they asking me to find in part A? It's got the R by itself. Now, kids want to cancel an R. No, no. One's on top, one's on the bottom. In fact, when I move both of those guys to there, I'm going to have an R cubed. A T squared up here, a 4 pi squared down there. Right? Stuff moves diagonally. So we'll have this.  I want to get rid of a cubed. OK. R is going to be the cube root of, and this is about as long an expression as you'll end up typing in this year, 6.67 times 10 to the negative 11. The mass of the planet just 6.36 times 10 to the 30th. The period, 57,600? Yeah. Squared all divided by 4 pi squared. I would do what's inside first and then cube root. Can I get a radius of 3.3 times 10 to the 1, 2, 3, 4, 5, 6, 7, 8, 9? By the way, what if instead of asking you for the radius, what if I'd ask you for the height or the altitude? Take that number there. And what? Look too far, Mr. Duke. Subtract the radius of the planet and whatever's left is your altitude. Now, in this case, the radius of the planet is so small and this number is so big, you won't notice much of a difference. But I'd pick better numbers on a test because I just made these up. But for what it's worth, if you wanted to find the altitude above the surface, just subtract your radius from the radius of the planet. Whatever's left is how high above you. B, orbital speed. OK. We would go, well, sorry, Mr. Duke, don't take shortcuts. We would again go gravity equals circular.  Once again, that's cancels. This time, one of the r's cancels because there's two on the bottom on one side and one on the bottom on the other side. Let's see, do I know G, 6.67 times 10 to negative 11? Do I know the mass of this mystery planet? Yeah, 6.36 times 10 to the 30th. Do I know r? Hey, what did I figure out in part a? How would I get the v squared by itself? Square root. So we won't solve this. I'm just going to say for what it's worth, it looks like v is the square root of big G, big M, over r. Can you see, though, I could also have given you how fast the satellite was traveling and said, find the radius? Or as a two-step question, given you how fast the satellite was traveling, and said, find the period, you'd find the radius first, and then you'd go to this one, but instead of solving for r, you'd solve for t. But I gave you the period and the questions. In other words, you know one, you can find the other two, whichever one they throw at you. How do I know to use that approach? Have they mentioned in the question, work anywhere? Did they mention energy anywhere? Do you see a change in height anywhere? That's how I know it's forces. And the flip side of that is, by the way, if they mentioned work or energy or there's a change in height, you're probably using energy. Gravitational, potential, energy, energy, energy. Probably this is what you guys are wrestling with. I agree, it's not a tough topic, it's a confusing topic. You really gotta keep stuff straight. Can you remind me at the end of class today, who's in my Block C class? My Block Bs, I went through the review and said, I like this question, I like this question. Did I do it with the Block Cs or did I forget? Can you remind me to do that at the very end of this and we'll tack that on to the video also? I'll give you a few hints since you're here. I defined, that is on your formula sheet. Why negative? Because we said that if you have potential energy, you want to fall. If you're out at infinity, do you want to fall? So how much potential energy do you have? Desmond, can you contact Local 202 please, Desmond? And if you're closer than infinity, you must have less energy than zero. Oh, you have negative. So what kind of questions can we ask you? Well, let's see if I can find a couple. First, I'm gonna expect, I can simply say, find the potential energy at a specific altitude or height or radius. That just crunches the numbers. For whatever planet I give you or whatever satellite we're dealing with. But usually what we're doing with this is stuff that involves work. So let's see, I think now we're gonna try and pull some of these out. Please tell me this was my potential energy loss. Hey, it was. Let's grab some from the home of Mr. Derrick. So let's go, says calculate the orbital potential energy of a 12,500 kilogram rocket on the surface of the Earth. Why do they say orbital potential energy? They're saying don't use MGH please. Use the Cosmic. I would say potential energy equals negative big G, big M, little M over R. Have they mentioned a change in height here or anything like that? No, it's not work. I'm not moving something. G negative nine, sorry. G 6.67 times 10 to negative 11, big M mass of the Earth, little M mass of the rocket, R radius of the Earth, that distance. I'll assume you can crunch those numbers and you can check your answer. I'm more interested in the next couple of questions after that, but I figured it was better if I started with those two. So bear with me, I'm gonna go clip. A 12,500 rocket ship on Earth at rest blasts off and reaches a height of 2,000 kilograms, kilometers above the Earth. Now I got a problem because it's kilometers. I would right away say offer Pete's eggs. Two times 10 to the sixth meters. Ooh, above the Earth's surface. So when I wanna find the radius, I'll have to add the radius of the Earth as well. A says, find the final potential energy.  It's gonna be negative 6.67 times 10 to the negative 11. Are we Earth yet? 5.98 times 10 to the 24th, 12,500 divided by, what's my final radius? Well, it's an altitude of two times 10 to the sixth, but I also have to include the radius of the Earth. That's my final distance from the middle of the Earth. Is that okay, Brandon? Could you type that in and get the right answer? Then I won't worry about it because the answers are there and part of your homework anyways. B, find the work done by the rocket engines. Okay, work. I can't use work equals force times distance because the force is not constant. The further you go from the planet that we could grab it again. So I have to use another definition of work. We said that work was, this is not on your formula sheet. Gotta have it here. We called this the work energy theorem. I think though I can in this case do that because if I'm reading this correctly, it starts at rest, right? So initial kinetic is zero and they're not putting an orbit. They're lifting it up to an altitude and then little invisible angels or whatever are holding it there because if they let this rocket chip go it's gonna fall back down. So I think it's final kinetic. It's at rest, it's also zero. What's changed in anything? So you're gonna get this. Negative big G, big M, little M all over our final, which is two times 10 to the six plus 6.38 times 10 to the six minus negative big G, big M, little M all over our initial, which would actually be the radius of the earth because that's where you started out. What do you see here, Pat? A minus minus, which is a plus. In fact, you're gonna get a positive answer because all the top numbers are the same but this is a way bigger number than that. The negative number will be way smaller because you're dividing by a bigger number. You'll always get a positive work. You should because the spacecraft doesn't want to go up there. You have to supply energy. You have to put in a positive amount of energy to get it up there, the rocket fuel. So you will get a positive answer. Is that okay? So what if you let go of that rocket? Well, in this case, we have a similar question. We have a 1200 kilogram mass and it's released from a height of 4,500 kilometers above the earth. Can I just clue in? I think this is 4.5 times 10 to the six meters. Oh, above, so I'll have to add the radius of the earth. It falls to the earth as no external force acts on the object energy is conserved. It says, first of all, write a work energy equation. I'm not gonna do that. Find its initial potential energy, okay. Negative 6.67 times 10 to the negative 11. I'm gonna try plugging in the numbers right away.  What's my initial radius? Here we're not starting on the ground. We're starting up in space. So my initial radius is gonna be 4.5 times 10 to the sixth. That's the altitude plus the radius of the earth. That's the total distance from the center of the planet. That there is your initial potential energy and it's gonna be negative. What would its final potential energy be when it reaches the earth? It would be this, but in the denominator, all I'd have was 6.38 times 10 to the sixth. I'm more interested, part D is kind of nice. How fast? Do we have a change in height? Are they also wanting speed? Conservation of energy. Potential energy initial plus kinetic energy initial equals potential energy final plus kinetic energy final. And I'm pretty sure it's starting out at rest because it's released from a height. But I don't think any of the other ones are zero. I think you're gonna have negative big G, big M, little M all over 4.5 times 10 to the sixth plus 6.38 times 10 to the sixth. That's my R initial.  I'm just showing you the numbers that are gonna change in the interest of time.  I've scrolled down, but however much it weighed. Your final radius would be the radius of the earth plus kinetic energy, far. So what's kinetic energy final? One half M v final squared, which I'm pretty sure is what they want me to find, isn't it? That's, if that's our final height, that's our velocity at that height. Yeah, that's when it hits the earth. No, no, no, no, no, no, no, no, because the force is changing, gravity is changing. You can't use MGH because we're going cosmic here. No, no, no, no, no, no, no, no, no, no, no, no, no, no. No, no, no, no, no, no. By the way, if you used MGH, you'd get a zero here, which would totally skew the question. You have a question or was that just, okay. Third type of work energy question. So the first one, here's variations on lifting it in orbit. The third type is lifting it and putting it in orbit, which means you're going to give it potential and you're going to give it kinetic energy. See if I can find one. I mean, I've glossed over some details, but eventually you are gonna have to look at your notes and do some homework and I'm going to help you part of this, I'm also bailing out, not, I don't know if it's you guys, but I'm bailing out a bunch of kids that did no homework for the week before spring break and then no homework during the basketball tournament. I recognize that.  Some people have made decisions that might affect the grade. For me, you made a positive decision, but I'll give you a shovel, I'll give you instructions on how to dig out of the hole, but I won't throw any dirt for you. Okay, so here's a classic. Number five from lesson seven. We'll just talk about it. Okay, by the way, the author here uses RTZAI, that's relative to zero at infinity. What he's saying is use the cosmic potential, not use MDH, right, that's our hint as well. So could you find the potential energy of the satellite on the surface of the earth?  Could you find the potential energy of the satellite when it is in orbit?  Could you find the orbit speed and the kinetic energy of the satellite? Didn't we a few examples ago when I did FG equals FC? Couldn't I use that to find your orbital speed if I knew the radius? Oh, and once I know the orbital speed velocity, kinetic energy is a half MV squared, yes? Could you find then the total orbit energy? Sure, it would be whatever the potential was up there, plus whatever the kinetic was up there, and it would be negative, because to get out to infinity, you'd have to add energy still, and then find the total work. So let's try this puppy, and I think this might be what we'll finish with, so I hope I think that one. This is a better question, let's do this one.  Remind me though to go through the sheet and tell you which questions I like, okay? By the way, so look at this question here, where they give you the mass of the satellite. Once again, he does 5,000 kilometers above. Once again, I'm gonna go, that's five times 10 to the sixth meters. I could ask you E without walking you through everything else. If they just said, hey, how much work? The work to put something in orbit is the change in potential plus the change in kinetic. If you're lifting something and holding it there, your change in kinetic would be zero, and that's why we just did change in potential. But if we're going in orbit, that's a fairly long question. We would need to do change in potential and change in kinetic. Let's do A, first of all. The potential energy on the Earth, I'll call that initial. That's gonna be 6.67 times 10 to the negative 11. 5.98 times 10 to the 24th, 10,000, divided by 6.38 times 10 to the sixth, and except it's negative, I forgot the negative. Woo, that was sloppy. Would you be able to crunch that and get an answer? Then I'll trust that you can. B. What would the potential energy be when we're in orbit? Gonna be the same, the same, the same, all over 6.38 times 10 to the sixth plus an altitude of five times 10 to the sixth. That's the only difference, which means you could probably go second function, enter on your calculator, and just change a couple of numbers and I'll have to retype the whole thing. C says, find the orbit speed and the kinetic energy.  They gave me the mass, I've scrolled down, but I'm pretty sure they gave me the mass. Yeah, 10,000. Really, what C is saying is find the velocity, and I would have no problem as a question giving you the same information and then simply saying, tell me the kinetic energy in orbit. And I'd assume that you'd clue in, I gotta find velocity, because that's really what this question is asking. How do we find speed? Do I wanna use the one with speed or period in it? Yeah, v squared equals big G, big M, or let's see, type, type, type, type, type. Oh, and this is actually kinda nice because it looks like the kinetic energy technically is one half M, big G, big M over R, because if I square the v, I just lose the square root. In fact, big G, big M, little M over R, if there was a negative there, that would be half the potential energy, but negative. We said you don't memorize this, but for what it's worth, if you wanna know how these are all interrelated, as it turns out, the kinetic energy of a satellite is the same as its potential energy divided by two, but positive. Just is, because they're so related together. Oh, and then D, total orbit energy. So if they ask for total energy, how does the word total mean to you mathematically? What mathematical operation do you think we do? It's gonna be the potential energy in orbit plus the kinetic energy in orbit. It would be the answer that you got for B plus the answer that you got for C. And there is a shortcut you actually find as it turns out, the total energy in orbit is half the potential energy, but negative. You don't have to memorize that, but if you're doing it and you say, hey, wait a minute, I know that's exactly half of that answer up there, you can probably, I probably did it right, okay? I hardly ever use that shortcut though. I usually prefer on a test to take my time and get it in a nice, comfortable way. And then E, the work, work is change in potential. You go that minus that, plus change in kinetic. Your final kinetic is this bad boy here, your initial, zero, because you're starting from rest. And you add them up and that's your work. And you would get a positive answer because absolutely it requires you to do work to get a satellite in orbit. That doesn't cover all the bells and whistles, that covers the bulk of it. Then you can look at the review and look at my solution key and figure stuff out. Now, questions that I like. From the review, I'm gonna hit pause for two seconds. So a couple of hints, I've already said, please be prepared in the gravity formula to solve for mass or for radius if you know the force. There's a couple on here that I do that. A classic example would be, for example, to say there's a satellite orbiting the Earth. If I know the force that the satellite feels, can you figure out how heavy this, but what the mass of the satellite is? You know the mass of the Earth, I tell you the radius, et cetera. Bear with me, bear with me. I'm trying to find a specific one that I can't. It's a multiple choice, so I'm not gonna freak out if it's a bit tricky, but okay. Let's take with the program, Mr. Dewick. Which ones do I like? You should definitely understand stuff like number one, the conceptual stuff. Which way is acceleration, which way is velocity, which way is force, okay? I think there's a bunch of those in the review. So I'm not just gonna say I like them more, I like, there's gonna be a conceptual question where I ask you about direction. Sorry while I'm hesitating and having to remember. Something like seven is fine, eight is good. I like eight, 13 is nice. Again, 14, another conceptual, like make sure you understand that force and acceleration are inwards, velocity is not inwards, velocity is 90 degrees. Make sure you know those. There's some kind of an amusement park ride that's prepared to handle like 16, a Ferris wheel or something like that, okay? I believe I put a horizontal circle somewhere on here like the conical pendulum, like number 18. And remember I said as twists, instead of giving you the mass, I would have no problem giving you the tension. Or other stuff I can muck around with. Oh, you don't wanna click there. Make sure you can figure out gravitational field strength, remember gravitational field strength was big G, big M over R, so gravitational field strength of Mars or of a planet or of the moon, something like that. 23 is good. I like, make sure you understand how the graph works. Oh, there's what I was looking at. Sure, 24, where I said I'd give you one where I'm gonna either ask you to find a mass or a radius. So here's one where you know the force and you gotta find something else. Okay, I knew I had one on there somewhere. Or even 25, I'm noticing 25, they're asking you to find the mass of the planet as a twist. Instead of saying find the energy, I find the planet. Okay, be prepared for something like that. Oh, that was a lot. Sure, there's one similar, that's scaring me. 42 is good. There's some kind of a question about graphs. Well, there's some hints, anyways. There's others. The test, I'll even give you more specifics. Test is mostly multiple choice. It's 11 multiple choice. And then one, two, three written. There is a using principles of physics kind of a question on it. But I think you'll find the multiple choice probably is the more challenging. But if you've done the review, I can't say this time that you'll have seen every question. You'll have seen every type of question, but be prepared for me to give you one more. Oh, that's backwards from the way they asked on the review. They went forwards, I went backwards. That kind of a thing. Is that okay? Do you have any specifics that you wanted me to do? Or is it better, you know what? Probably better for you to work through some of this on your own now. And then if you have specifics, I'll probably do 10 minutes at the beginning of each class, okay? I'm gonna hit save, first of all.


So, for our next talk, we have someone special joining us. You know, so this person who I'm going to introduce is like one of the funniest people I know. And you know, I see I sometimes secretly wish I was him. So, so let's welcome that person now. Okay. Hello everyone. It's my talk right now. Thank you for that humbling introduction. My name is Sangarshan. I work at Grofus and it's pronounced grofus. So I like building imaginary projects in my head talking about those imaginary projects in my head. And, you know, I also love all those imaginary projects. So I'm going to be talking about one such case where that imaginary project actually got executed and which was amazing. So that is the story of this is the story of how I did that. So I'm going to begin by proclaiming my love for pandas. You know, whenever we want to work out whenever almost all of us want to work with data. We know we move to pandas and you know rightly so pandas is amazing. It's like the Tom Hanks of Python libraries. And of course, it rests on top of all these amazing. You know, packages which are present in the open source environment. These include, you know, matplotlib. We have NumPy. We have pandas. And then we have scikit-learn. You know, all these amazing open source packages from the scientific Python community makes Python the code to language when anyone wants to do anything with data. So we're going to talk about a special type of data, which is location data. Location data has location component linked with it. For example, I'm reading a CSV file over here, which has latitude and longitude. So this is essentially a location component. So a data with a location component can be represented as a geometry. And there are, so geometries are basically just X and Y coordinates and the various ways you can arrange them. So these geometries can be a pair of lat-longs or they can be a list of lat-longs, just a polygon. And also I am grossly over simplifying what geometries are and Euclid would be really angry with me right now. But we also have line strings, which are like line strings. And we have multi-polygons, which is a fancy plural word for polygons. And we also have circles. Now, to work with these geometries, we have this amazing package in the open source community called Geopandas. So with Geopandas, we can work with data frame. And in this case, a geodata frame. And, you know, we can stay with a familiar interface. And Geopandas will let us read and write commonly used geospatial formats, like, you know, KML files, shape files and geochasin files using the other library called Fiona. And then we also can perform different spatial operations, like merge, overlay and joints with the help of another amazing package called Shaping. And also, of course, the crux of the talk, we can plot them on a map with matplotlet. And also, I'm leaving a whole, whole lot of things which we can do with Geopandas, like, you know, handling projections and recently added stuff like vectorized operations with pygeos and also indexing your data with, you know, our trees or any other data structure. And if you are interested in knowing more, this is a tutorial link which I have attached here. I will share these slides on the, on the break room. And this, this tutorial has been made by the maintainer. So it's like pretty comprehensive and it's pretty amazing. All right, so moving on to data frame. So we have this data frame which I read before. And we have lat and lawn. So now we convert it into geodata frame. So how we do that is we import Geopandas and also we convert this lat and lawn column into a point. A point is a geometry. So we set geometry equals combination of these two columns. So it creates a column called geometry and it creates a point, a point geometry object using shapely. So this is that point. And also, on the second line, we are setting something called, you know, CRS. So CRS is the coordinate reference system. So this is how we project our earth in a way that we can understand and interpret. So in these cases, so in this case, we have used ES, EPST for 326, which is like the most commonly used coordinate reference system, which is also used by GPS systems and all the navigation systems. So this is the reason why lat, latitudes and longitudes have spatial meaning in them. If not, if you don't have coordinate reference system, they are just arbitrary x and y coordinates. They are not latitudes and longitudes. So how do I plot them? So with Geopandas, everything becomes really simple. It's just a dot plot. So you just do import map plot lat and then you just, you know, So to do interactive maps with Geopandas, we actually have to move away from Geopandas and into other amazing open source libraries, which are there for creating interactive maps. So how do we do that? Do that we employ the most powerful weapon a developer has, which is Googling. So that's what I did. I just Google for a while and you know, I actually got to know that Folium is actually one such package that actually lets me do this. So I take in the geodata frame and then I import folium and then now I create an folium dot map. So this folium dot map is just an empty canvas, kind of like a canvas where you can draw on top of. So this just creates a dummy map for me where I pass in the location, the zoom start the tiles and also we have various other parameters you can pass to the map. So after creating that dummy canvas. Now we want to plot our data on top of this canvas. So to do that, we create a feature called points. So these points feature is made up of geodata frame, which we created before. And also we had a parameter called tooltip tooltip is also a feature in which the field is named. So when I hover over this map, I can actually see the name of each and every point that I just plotted. Now after creating this feature, I take the canvas and I add this feature to the canvas. This is a very simple and incredibly effective to create, you know, beautiful looking maps. Now, onward to polygons. So we again read geodata frame, which is made up of polygons instead of points as you can see it's made up of multi polygons, and also polygons, and these are all different, you know, countries and continents. So to create a map out of them with geopandas, we just again do just dot plot pretty easy. And we now choose the column which we want to plot on top of, for example, here I've chosen GDP. So that means this map is colored based on the GDP. And also, we pass the color map so that you know it goes from this color to that color. I have also attached a link for the color maps, you know, the different color maps for macro which are present, and also I give legend equals true so that I actually see this. So now onward to the interactive maps to do that first, we actually create this color map to do that I'm using another package called Brankar dot color map, using which I'm actually importing this color map. And then I'm passing the number of steps I have to split it out of. So after creating the color map, I define my empty folium canvas. And also I define a style function. So this style function contains the various parameters that I'm going to be passing to my map, which I'm going to create right now. So it's made up of a fill color which denotes the color which I have to fill in that particular polygon, and also the color of that polygon itself, and also the weight of that border, which is the polygon color, and also how much is the opacity of the color I have to fill it into. So these are the parameters. And then we again we create a geojson feature, we pass a Julia frame, we create the tool tip and this time I'm passing the name and also the GDP. So when I hover over it, I see both of them. Amazing. So I also pass in the style function and then just add it to the canvas and also notice that I add the color map to the canvas. So I see this incredibly distorted legend, but I still see. So folium also has several special maps that you can actually create with it essentially. So these are called plugins that you actually create with these. So one such plugin is called market cluster. So with market cluster, you just, you know, import a market cluster from folium dot plugin. And now, I think a little weird, where you're bearing you need to take a geojson frame and convert it into a list of latitudes and not so we do that over here. Now we have a list of lat lungs. And now we create an empty canvas.   So, so these two, the number two here means that this cluster is made up of two points. So the number eight means that this cluster is made up of eight points. And the cluster 76 means that this cluster is made up of 76 points. So I can click on it, it splits into several clusters again, I click on it, it splits into clusters still I'm able to see each and every individual point, which is pretty awesome. Now, heat map. So heat map is something which, you know, given the current situation we actually see on a daily basis. So we know how important they are to convey the message, you know, so this is the heat map we're creating. Also, this does not represent anything, this is just arbitrary heat map to do this we you know take the location and you know just create a heat map out of it with a radius of this particular map. Heat maps actually are pretty interesting because so you just have to take one look at it, do you know, get all the information out of it essentially. So these are pretty cool. So now more data and more problems. So one issue which I started to notice, you know, when going down the folium path is when the number of points in your map start to increase. Folium starts to get a little bit ineffective. Folium cannot handle a lot of points. So one such also one solution, which you can deploy to make folium actually handle a lot of points is to actually, you know, create clusters like this, you know, create clusters so that you can actually plot out of points. But in some cases, the number of points you have, you know, you know, is like a lot. So your DOM will just crash like your browser crashes and you will not be able to plot all these spots. So that's where things get a little hard. But no fret not, we have a new kid in town, and that's Kepler GL. So this is the textbook definition of Kepler GL. So essentially it's this amazing project, which was developed at Uber. So they have built Kepler on top of that GL and the GL. So, you know, they actually can render, you know, millions of points and perform spatial aggregations on the fly, which is pretty amazing. You know, and you can create, you know, amazing cool looking maps with Kepler when you want to scale out your points or scale out your data. So to install Kepler, when you are on a Jupyter notebook that's greater than, you know, the version 5.3, you can just do a pip install Kepler GL, it installs it.   So another amazing thing about Kepler is that it uses configs to customize the maps. So a config looks like this.  So I'm not going to go really deep into that, but I'm going to actually give you an overlay of, you know, all the things that you can control with the config. So Kepler's UX flow is actually made up of five layers. So initially you have your base map, right? So the base map is made up of tiles that you can acquire from various sources. For example, you have, you can acquire tiles from open street maps, you can acquire map tiles from Google, you can acquire map tiles from Mapbox, you know, several styles, and you know, that makes up your tiles.  And also on this data, you can perform filters, aggregations, and, you know, all the lot.  So we have hexagonal layers, we have arc layers, we have point layers, we have path layers and we have grid layers. And the amazing thing about it is that these layers, like some of these layers are actually, you know, interchangeable, like for example, you can have a point layer that you can represent as a grid. And you have, you know, H3 grids, which are actually a spatial indexing system, which is also developed courtesy of Uber, which, which can, you know, help you plot a lot of points without having to actually show those points on a map, rather index them and aggregate them as grids so that, you know, the number of points in your map significantly decreases. And also you have interactions you can perform on the data that has been brought on a map. And these interactions include stuff like tooltip. For example, these, the tooltips are the ones which I showed before, where you hover over component in a map and you know, you see the name or something a little bit of that particular geometry. And also Kepler has these interactions like, for example, you can geocode a particular location by just, you know, using an interaction, you have brushes, and you know, you have also the coordinate, you know, interaction. So given the customizability of Kepler and, you know, given the amount of layers it can process you, you can actually see one in action right now, where, you know, with an aggregation of points is getting performed on the flight. So we're just choosing a color and we're choosing to color those grids based on a particular field, which is actually getting done pretty fast. And also this is one of the things I absolutely love about Kepler is how amazingly beautiful spatial temporal maps you can create. So a quick definition of spatial temporal maps, a spatial temporal data is when you have both space and time linked with a particular data, which is pretty cool. So an example of this can be a trip or a practical example would be a drone data, right, so you have a drone that you're flying around. And at, you know, when you get the data out of that drone, you actually have two components of where it was, and when wasn't there. So you can use this information to create a timeline chart using Kepler and it looks as beautiful as this. So this is actually a trip data. So you can see trips over time, it looks, you know, pretty beautiful if you can create. But as always, you know, these are not the only libraries that are there and given the amazing community that is present in the open source world. So you can actually, you know, we have like tons of libraries that you can depend on. You don't have to just, you know, you have countless libraries, that's what I'm trying to say. So I'm going to just explore them. The next library is to book it. So with okay, you can actually do something similar. So here I'm just, you know, importing the figure, the output file and I'm importing the tiles. I'm using carto TV styles, which is, which is going to be my base map provider. And you know, I'm just creating an empty map. So here I'm actually choosing my coordinate reference system, which is marketer. And also I'm providing the range of the X and Y, which is, you know, pretty interesting and is not a feature that you have in the other libraries.  And, you know, it, it's good to actually explore this, it's actually fun to explore these libraries, you know, and how people are doing the same thing, but in really different and really amazing I know, and also we have plot, a plot list, a plot lead bouquet are not just for maps, but for, but for, you know, just basic interactive plots. And also we have Altair. So over here with partly I'm actually using partly express so that this code is a little smaller with partly it gets a little bigger. So with partly express I'm importing the car share data set, and I'm creating a scatter map box plot by just passing the data frame, the latitude longitude, the color and the size. So here actually, this is pretty cool because I'm able to represent more than I would be able to represent normally. So I'm using color to represent a feature, and I'm using the size to represent another feature. So I have these two features complementing each other on the same map. So this is really useful in cases where you want to, you know, spot correlation between two events happening, link to the same spatial component at the same time. So it's cool that you can do this with plotting. So this talks about your pattern, which is something I worked on on my free time, which is kind of like a hack function of all the scripts that I wrote to quickly create interactive maps, but without going to other libraries by staying in the realm of your data frames essentially. So it's something like so, so if you have not cringed yet a geopatra is named geopatra because it rhymes with Cleopatra, and you know, a Cleo and geo, you know, kind of rhyme and you know, I thought I was being clever at the time. So to create a folium plot, you just import geopatra and you do the data frame dot folium dot plot, and you just plot it. So it's just a single line to, you know, plot your geopatra. Oh, but you know, one thing which you know even I thought myself while just writing this is, why can't they just be these scripts which I keep for myself and why does it have to be another library. It can just be a gist of, you know, functions that can, you know, plot visual effects, not a library, right. So again, it's not a library. It's a wrapper essentially, a gigantic wrapper. And it's an interface, an interface to interact with the existing libraries without leaving the geopandas ecosystem. And also I have Netflix syndrome. So if you don't know what that means, Netflix gives you a lot of choices when you open the app and you know people get really overwhelmed at that choice and it's really hard for you to choose something. So it's the same thing for me, you know, there are these amazing libraries, you know, which complement each other, and also they are different in their own way and I don't want to choose one of them. I want all of them. And also, I actually want to spend more time plotting and, you know, spend less time googling for APIs because I have a very bad memory and I tend to forget, you know, how do I create a chloropath map is fully how do I create a heat map. I just keep googling and, you know, for different packages and you know that sometimes gets tiring. So, oh, alright, so let me move to the documentation of geopandas essentially. So with geopandas, you can I'm actually just taking these two data frames out, and I'm creating these interactive maps. These are the geochason maps. So this documentation is at geopatra.readthetalks.io and the GitHub repository is GitHub slash Sangashnan slash geopatra. So since my name is really weird, like, I actually get my name to be the username in every platform that I go to.  So I created geochason map with just one line. I create a circle map with just one line. I pass the parameters of the tooltip, which is named so that I hover over it actually see the name. And also I have the radius, which is the radius.   So these are the chloropeth maps, which is again one line. You color by the population, instead of the GDP, but they are obviously correlated. And the tooltip is the name so I hover over it actually the name. I, you know, set the color. I set the zoom and I set the style. And the marker clusters are again one line. I create the marker clusters. And I also have weighted marker clusters, which are kind of in, in the experimental phase essentially. So these are the ways where you can cluster with not just points, but with value. So these two means there are two points, right. So the cluster clusters mean that when you go here, the sum of the values here, you know, account to 986. It's not essentially the number of points. And you know, they look really weird because it's not completely ready yet. I'm just playing around with things. So, and also, of course, we have the heat maps that are always there. And, you know, this is what I'm actually excited about, which is Kepler. I also have a way to create an interactive map with just a single line, which is, you know, again, the data frame dot Kepler dot plot.  So I'm actually controlling the conflict of Kepler with, you know, a ginger template essentially. So the parameters you pass here just replace those prebuilt templates which are there. And you know, it's pretty easy to plot them actually. So to create a simple polygon, I pass the color, I pass the stroke, which are now a list of RBG's, but they will not be really soon. I have a PR ready to, you know, make them into actual colors rather than passing a list of RGB's. But for now, they are. And also, I pass the stroke thickness, which is a parameter I pass the opacity. You know, to create this plot again. So now they are all the same color, right? I can also pass a new parameter called color field, which is the population estimate and I also pass the color scheme, which is blues. So right now, because of this, it is actually colored based on the population estimate rather than being colored arbitrarily. So yeah, that's it for Geopatra. And thank you for coming. Okay. I'm just going to look at the questions. Okay, I have two questions. Can you talk about how Kepler is better than Mapbox since it's built on top of it. Okay. So even Mapbox are actually complimenting like one is not better than the other essentially. So actually Kepler uses Mapbox internally to be honest. So, Mapbox is the tile provider for Kepler. So the base maps which you see when you want to create plots on Kepler, they are all Mapbox tiles. So it's not kind of a competition, but kind of complimenting each other essentially. So yeah, that's that. Also, another question, do either Folium or Kepler support non geographic map, for example, mapping a star map. I'm not, I'm not sure about Folium, but with Kepler, you can actually provide your own custom base map. So if you actually Google for it, you can actually find a map where people have plotted a baseball stadium and where they have actually modeled the whole stadium on the base map and plotted how different shots have flown. You know, the shots which were hit and the different trajectories they had gone into. So like that was pretty cool. So, so I guess it is possible, you know, where you can pass your own custom map custom tiles and create maps out of it, but it is actually pretty hard to do. But it is possible, but they are mainly present for geographic maps, that's their main use case, but it is possible to extend them and customize them and of course the code is all open source. So all the projects I talked about are open source. Are there any map packages that also integrate AR functionality. So I assume you mean augmented reality. And to be honest, I don't know I have not worked with AR maps. So I, I just have done stuff with your unity and euphoria, which is a pretty basic so I'm not really sure I can actually maybe Google for it, and you know, get back to you or we can discuss about it. So, okay, I think that is it. We are out of questions. Thank you very much, everyone. Thank you for joining. I hope you liked my introduction. That was something I was planning for. And, you know, thank you for being with us.


Baby talk about endless compliments Another video if you're new here, my name is Cara do not forget to like comment and subscribe So as you can tell by the title we are gonna be talking about fragrances today. I love talking about fragrances I love that I love sense. I love that they just leave a memory I love that it can leave a memory on someone and there's always a story to tell behind a fragrance We're just gonna hop right into it. So if you want to see my suggestions, just keep on watching Before we hop into the video, I do have to talk about today's sponsor, which is rebel sense I've worked with them so many times. They have affordable luxury perfumes girl up to 60 percent off They have perfumes from Le La Vo, Baccarat, Jimmy Chu, YSL, you name girl, they got it including men So make sure you check out the men's section. Okay And also if you're somebody who doesn't know where to start when it comes to fragrances They do have a fragrance quiz on their website and they will give you perfume selections So you don't even have to think about a girl. They will do it for you. And that's just period.  Whatever scent family you like shopping from they got you Make sure you check out rebel sense and also they do have payment options available They do have collerna, which is a four interest free payment plan And also if there's a discount code, I'll have it on the screen for you. Thank you so much rebel sense for sponsoring this video I love their website. So the first scent we're gonna get into is one of my favorites I cannot not layer this scent with another scent. It's the perfect Warm scent like I told y'all I love Warm scents and this is the replica jazz club by mason Margiela Girl, I had to read up shout out to rebel sense because This is just the perfect Warm and sexy scent like just picture yourself get in all dress And then you're about to go to a dark and sexy ambiance Girl, this is what you want to put on and not only do I like to wear by itself It's it's so good by itself. It's so good But I love to layer this and it just enhances Every single scent that I wear literally look at my bottle I Love this like if I was a scent this will literally be my number one jazz club because it just smells So good so rich and when I tell you if you layer this with any other scent Chef's kiss, it's gonna just enhance it even on here for the style description It says memory and a fragrance literally you leave a memory on somebody that walks past you Every time I wear this I get so many compliments. They're like, what are you wearing? It's honestly this top with something else.  You can get this on rebel sense for a 129 99 in a retails for a 144 I would never get enough of jazz club rebel. Never So good. I had to start off with that one because it literally layers with everything I'm about to talk about so good especially one I'm about to get into so Let's just get into the next one. The next thing we're going to get into is onyx by rebel sense Love this thing. This is one of their best sellers. I remember getting this when it first dropped This smells exactly like ysl libre and it's long lasting so affordable. It's only 45 dollars and It just smells so good. And like I said this with jazz club Money money. Well, this is that girl boss saying I love it so much. It smells so good It's also in the musky and floral family It smells just like ysl libre the regular one and the notes on here are citrus raspberry And the heart is jasmine gardenia and the base is amber and honey such a beautiful scent Definitely girl boss vibes. Love it packaging even screams money with gold and burgundy And I love that it's so affordable and like I said rebel sense really just makes it really affordable for the girls to Not break their bank but still smell like money, you know, this next same girl. I Could not find this in anywhere. So I've never smelt it in person I just seen it all over the internet saying Oh, it smells like bakarot rouge.  This is what it's giving So and I love that it comes like this. I love the packaging. I think it's so cute. It's so teen appropriate So if you want to give your teenage cousin or somebody in their teens or somebody just you know wanting to smell like Luxury it's not overpowering if you're somebody who doesn't like overpowering sense grows out here That just don't like heavy frequencies and they have headaches from them This is something that you can definitely start off with because it definitely gives you that 540 vibes, but Not so intense. I see why it's called cloud because it's obviously light and airy So I feel like that's definitely a story behind why she named it cloud But she definitely hit it on the hay with this. I really think this is cute fun and flirty It's giving money vibes So the top note on here is lambda pear and bergamot. The heart is coconut Paralene vanilla orchid and then the base is cashmere.  Let me just Add it to cart, you know, let me just have that in my suggestions for the girls Just so I can have some bougie on a budget options So definitely highly recommend this super light and airy, but still gives you that luxury Money vibes. It definitely makes the perfect layering scent It definitely will pair beautiful with a vanilla scent or a cashmere or a woody or musky scent Love this if you are a girl boss You love captivating seductive Sexy Scent Baby why is so intense? They did it with this one. This is on a whole different level. Okay This smells so it's giving wealth. It's giving money It's so captivating the definition of grown in sexy This is something that you would only wear at night time Because it's just so intense like the name obviously and it just smells so Good this mixed with this baby Talk about endless compliments these two pairs together Oh my god, and you can get both on rebel cents girl. I sprayed it on the other day, baby What do you have on? What do you what do you have on? Oh? I'm telling you this combination this alone On top of anything will get you so many compliments. This is a girl. This is that girl.  This is also in the warm and floral family Which I love in the sense are the top note is lavender in essence The heart is orange blossom and then the base is warm Vanilla and this said last long as well too. So it's definitely worth the money and you can get this This is the 1.6 out. They have a 3.0 fluid ounces on there 1.6 in the 1.0 This 1.6 fluid ounce on rebel cents is the 102 dollars and it retails for 12 definitely hop on this it smells so good, especially for this season Especially at night time if you want to set the vibes. She's the one Not the two this next thing is rebel cents drip and gold This Is such an exotic sweet saying it just gives me eat me vibes. It's very gourmet. It's very Rich and sweet. You can really smell the vanilla and the coconut mixed together Did this to my sister one time and she loves it.   She's there But she doesn't have to do a lot before we even get into the scent Let's just look at the bottle. It just screams elevated sexy grown glamorous polished I love when my fragrance bottles look so cute because I love putting them on display and the spray dispenser is This cute little circle. How adorable is that? Oh Y'all This smells so good. Oh my god. This smells so good. You have to try out this jimmy chew. I want you It doesn't give me like Like fruity it gives me like elevated sexy grown poise You already know what i'm gonna say This mixed with the jazz club Uh I just like mixing fruity or something very like sweet with musky or woody I'm wearing this right now And I I've been a jimmy chew fan, but this is the next level. It's a showstopper. It's sexy If I was a fruity scent, this is what I would want to smell like So if you are somebody who doesn't like that overpowering of a fruity scent I feel like you would really love this like love this especially for the daytime Because sometimes I don't want to spell too warm during the day Especially when I'm going somewhere To like a business meeting or meeting up with people. I don't want to smell too overpowering, but I want you to know I'm here This this is the showstopper. She's a showstopper. She's stunning Oh, but the top notes are mandarin juice velvet peach the heart is red spider lily And jasmine in the base is vanilla and you can get this on rebel scents for a hundred and five dollars in this retails for 121 you're definitely going to want to spray this over and over again.  It just it's just it's that girl It's a showstopper and I feel like you definitely need to pick this up because once the girls know this is on rebel scents it's going to be gone So Oh god, this is this is so good. Like this. I'm probably going to be wearing this from the next couple days Um, because I just I just love it. Wow. This makes these two mix together. Like I said You got to a showstopper. So make sure you go grab this. This next set is miss guilty paris This is one of rebel scents exclusive perfumes. This gives me warm and spicy vibes Definitely perfect for a date night. The top notes are orange and green notes And the heart is tuberose honeysuckle and jasmine and the base is iris roots sandalwood and vanilla This is this smells like a subtle warm floral flower Smells super good super seductive very grown and sexy I definitely highly recommend this scent and it's only on rebel scents for a 49 99 So make sure you check this out. So this next set honestly only got it because of the packaging But when I smelt it This is the carolina herrera. Very good girl. Love the packaging. Let's get into it. It's a keel Love the shape. I think it's super sexy super soft super feminine And it's not overpowering just that good daytime scent that you want to smell good and very fresh and clean I just feel like it smells like a clean Like very sexy feminine woman.  It's very light and just delicate It's just super it's just like a comforting scent like you just want to smell good But not doing too much for the perfect girl boss super feminine does a lot of daytime things I feel like this is the perfect daytime scent The notes on here are red currant and leechy the middle is rose lily and the base is vanilla bourbon And I'm really shocked because sometimes I can definitely smell the leechy in a scent But I really don't smell it in this but like I said, it's very light and very daytime is And like I said, it's just a light Powdery fresh and clean daytime. It's retails for 79 dollars, but you can get this on rebel scents for 72 dollars Smells so good. Like I said before rebel scents does have men's cologne And obviously we're in the season of gifting looking to purchase a fragrance for a Male in your life rebel scents is for you and I have two scents to talk about today I have the Versace Dillon blue and then I have the rebel renegade for men I opened these and smelled them and I put them back in packages because I'm definitely going to be gifting them to Somebody in my life. First of all, I love that this is a set because I love that the shower gel comes with the fragrance Because I think that it's super nice and convenient to layer up On your fragrances, especially, you know for a gift It's masculine to the extent of being on a vacation. It's very clean Very light just smells super good But still soft at the same time like a man, but it's not too How many it's not too overpowering this set really smells like a vacation So I really love that this is a 1.7 fluid out and the body wash is 3.4 Perfect for travel. They can just throw it in their luggage and not even think about it Definitely check this fragrance out for them and this gift set retails for 88 dollars Wait, hold up. You can get this on rebel scents for 65 dollars for this gift set for the holiday season Like I said, and you can also sign up for kalarna For interest free payments. They make it so easy and convenient. That's why I love rebel scents and the family of earthy Woody the top notes on here are aquatic notes Calabrian barramot grapefruit fig leaves violet leaves patchouli the bases mineral months tonka beans and saffron Such a nice thing They have you to thank for that this next thing I'm about to talk about is a very masculine very masculine This is giving me old spice vibes But on a different level just smells very wrong man. I'm here.  It just gives you that ultra masculine vibe The notes on here are lemon and orange The heart is lily of the valley jasmine and the base is musk oats Moz if you know somebody who is very confident and like I say who loves to steal the room And it's only 39 dollars. So like I said, they have you to thank for that It smells so good. If you give this to your man, you're gonna want to jump on him You're going to want to jump on him for sure. So that wraps up this video I hope you guys enjoyed do not forget to like comment subscribe and leave a comment down below What since you'll be gifting this season and also what you'll be getting and don't forget to treat yourself Do not forget to treat yourself. Okay, and what's saying will you be getting? I want to know I'm telling y'all all these scents are so good and shout out to rebel scents Like I said, they got layla bow. They got baccarat.  So I love y'all so much and I'll see y'all next video Bye


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