8. Centripetal Forces & Gravitation

Uniform Circular Motion

1

concept

## Intro to Circular Motion

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Hey, guys. So up until now we talked about motion and forces. Everything's always been along a straight line, either in the X or Y axis or maybe at some angle like this. But now we're gonna start to see what happens when you have objects that move in circular motion. So in this video, I want to introduce you to uniform circular motion. Let's go ahead and check this out. So as the name implies, circular motion happens when you have objects, move in circular paths. The uniform part of circular motion just means that they're traveling with constant speed. So just imagine that you get and you start walking around in a circle, it could be counterclockwise or clockwise. It doesn't really matter, Right? So the idea with uniform circular motion is that the magnitude of your velocity, the number is always going to be the same, right? Constant speed. But because you are traveling in a circle, the direction of your velocity is constantly going to be changing. Remember that the velocity is a vector. So what happens is this. This velocity here changes direction in uniform circular motion and your velocity at any point along the path has a special name. It's called the Tangential Velocity. It's just a fancy math term, but the tangent really just means that it's a line that touches the circle only once and then keeps on going. One way you can think about this is that if you were walking in a circle and for some reason just decided to stop turning, then you would just keep going off in a straight line like this. And that's easier. Tangent. That's your tangential velocity. Alright, so because the direction of your velocity is constantly changing, there's gonna be some acceleration. Right? Acceleration, remember, is a change in the velocity could be either the magnitude or the direction. And so this this acceleration has a special name. It's called the centripetal acceleration. Centripetal just means center seeking, and the idea here is that this acceleration points towards the center of that circular path that you're making as two symbols. It could be a C, but some textbooks will also call us a RAB for radio. So the idea here is that as your velocity changes direction as you're going around the circle, your acceleration actually always is changing direction so that it points towards the center. So this is your centripetal acceleration. And again some textbooks will use a C or a rad. We'll just use a C now. Another variable that's important in circular motion is basically the distance from where you are on the set, on the path right in the circle that you're making towards the center. And that's really just if you're traveling in a circle, that's really just the radius of that circle. So we're just gonna use the letter Big are for this. All right, so these are three important variables here. We've got V A and R, and there's an equation that actually ties all of these up together. This equation is the equation for centripetal acceleration, and it's just v tangential, squared, divided by big r And just like any other acceleration, the units for this acceleration are gonna be meters per second squared. Alright, so let's just go ahead and get to an example. We're moving at a constant 5 m per second, right, so this is basically our velocity, and then when we turn into a circle of radius 10, so we have our equals 10. So the idea here is that you're walking and then also you just start to make a circle and we want to calculate this centripetal acceleration. Right? So we've got the radius, which is sen. And if you're walking in a circle, it doesn't matter which direction we just know. The value of your tangential velocity is going to be five. And let's just say it's in this direction here. So if you wanted to calculate the acceleration, then we're just going to use our acceleration equation. Acceleration is V tangent squared over big art, and we have both of those values. So we have 5 m per second squared, divided by the radius, which is 10. We have the right units, right meters per second meters. So we just got an acceleration that is 2.5 m per second squared. Alright, so that's it for this one. Guys, Thanks for watching and let's move on

2

Problem

ProblemA ball travels on a frictionless circular track at 3m/s. The ball cannot have an acceleration greater than 1.5m/s^{2} or it will go off the track. What is the smallest radius the circular track can have so that the ball stays on the track?

A

R = 3 m

B

R = 12 m

C

R = 2 m

D

R = 6m

3

example

## Circular Orbit of the Moon

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Hey, guys, we got a fun little problem here involving the moon's orbit. So we're told that the move and travels in a roughly circular orbits and we're told the radius of that orbit. Right? So this is the earth right Here is like little earth like this. You know, uh and so we have the moon that's gonna be traveling in a nearly circular orbit, which means it has some tangential velocity like this, and it has also some centripetal acceleration. Now we're told what the orbital distance is, basically between the earth and the moon, that's that's this big are here. And because of this really large distance, we also have a really small centripetal acceleration. So we're trying to figure out how fast the moon would be traveling if it's suddenly broke free of the orbit and then stopped orbiting to basically what this means here is that over three variables were actually trying to figure out the tangential velocity. Remember that the tangential velocity is the velocity you're going to have. If you were to suddenly stop turning in circular motion, right? Basically, it's just always changing direction like this. So if you were to suddenly stop turning in your orbit. You go flying off in this direction. So we're trying to figure out how fast what's the magnitude of that tangential velocity? All right, so basically, we're just gonna go ahead and look at our equation. We know that a C equals vis a vis tangential, divided by our which variable we're trying to look for. We're looking for the V tangential, so we're just gonna get everything over to the other side. Right? So we have that v tangential squared equals a C. Times are. And so now we just take the square roots. This is gonna be the square root of our centripetal acceleration, which is 0.26 and then our radius, which is 3.85 times 10 to the eighth meters. If you go ahead and work this out, you're gonna get about exactly 1000 m per second. And if you go ahead and look up or Google, what is the orbital speed of the moon? This is basically what you're gonna find. It's about 1000 m per second as it travels around the earth. All right, so that's it for this one. Guys

Additional resources for Uniform Circular Motion

PRACTICE PROBLEMS AND ACTIVITIES (16)

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- The radius of the earth's very nearly circular orbit around the sun is 1.5 x 10^11m. Find the magnitude of the...
- The radius of the earth's very nearly circular orbit around the sun is 1.5 x 10^11m. Find the magnitude of the...
- As the earth rotates, what is the speed of (a) a physics student in Miami, Florida, at latitude 26 degrees
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- The 10 mg bead in FIGURE CP8.69 is free to slide on a frictionless wire loop. The loop rotates about a vertic...
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- FIGURE P8.54 shows two small 1.0 kg masses connected by massless but rigid 1.0-m-long rods. What is the tensio...
- Suppose the moon were held in its orbit not by gravity but by a massless cable attached to the center of the e...
- A 200 g block on a 50-cm-long string swings in a circle on a horizontal, frictionless table at 75 rpm. (b) Wha...