Uniform Circular Motion - Online Tutor, Practice Problems & Exam Prep

Intro to Circular Motion

Guys, up until now when 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 going to start to see what happens when you have objects that move in circular motion. In this video, I'm going to introduce you to uniform circular motion. Let's go ahead and check this out.

As the name implies, circular motion happens when you have objects moving in circular paths. The uniform part of circular motion just means that they're traveling with constant speed. So just imagine that you get up and you start walking around in a circle. It could be counterclockwise or clockwise. It doesn't really matter. The idea with uniform circular motion is that the magnitude of your velocity, the number, is always going to be the same, constant speed. Because you are traveling in a circle, the direction of your velocity is constantly going to be changing. Remember that velocity is a vector. This velocity changes direction in uniform circular motion. Your velocity at any point along the path has a special name: the tangential velocity. The term tangential really 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, you would just keep going off in a straight line like this, which is your tangent, your tangential velocity.

Because the direction of your velocity is constantly changing, there's going to be some acceleration. Acceleration, remember, is a change in velocity—could be either the magnitude or the direction. This acceleration has a special name: it's called centripetal acceleration. Centripetal just means center-seeking. The idea here is that this acceleration points towards the center of the circular path that you're making. It has two symbols: it could be A_C, but some textbooks will also call this A_rad for radial. As your velocity changes direction as you're going around the circle, your acceleration always changes direction so that it points towards the center. We'll just use A_C here.

Another variable that's important in circular motion is basically the distance from where you are on the path in the circle that you're making towards the center. And that’s really just the radius of that circle. So we're just going to use the letter R for this.

These are three important variables here: V, A, and R. 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_tangential² divided by R. Just like any other acceleration, the units for this acceleration are going to be meters per second squared.

So let's just go ahead and get to an example. We're moving at a constant 5 meters per second, so this is basically our velocity, and then when we turn into a circle of radius 10, so we have R equals 10. 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. We've got the radius, which is 10. 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 5, and let’s 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 V² / R, and we have both of those values. So we have 5 meters per second squared, divided by the radius which is 10. We have the right units, meters per second and meters. So we just get an acceleration that is 2.5 meters per second squared.

Alright. So that's it for this one guys. Thanks for watching, and let's move on.

A ball travels on a frictionless circular track at 3m/s. The ball cannot have an acceleration greater than 1.5m/s² 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

Circular Orbit of the Moon

We got a fun little problem here involving the moon's orbits. So, we're told that the moon travels in a roughly circular orbit and we're told the radius of that orbit. Right? So this is the Earth right here. This is like a little Earth like this. You know? And so we have the moon that's going to be traveling in a nearly circular orbit which means it has some tangential velocity like this. It also has some centripetal acceleration. Now we're told what the orbital distance is basically between the Earth and the moon. That's this big R here. And because of this really large distance, we also have a really small centripetal acceleration. So, we were trying to figure out how fast the moon would be traveling if it suddenly broke free of the orbit and then stopped orbiting. So basically, what this means here is that over three variables, we're actually trying to figure out the tangential velocity. Remember that the tangential velocity is the velocity that 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'd go flying off in this direction. So, we're trying to figure out how fast, what's the magnitude of that tangential velocity. Alright? So, basically, we're just going to go ahead and look at our equation. We know that a c = v t 2 r . Which variable are we trying to look for? We're looking for the vt, so we're just going to get everything over to the other side. Right? So, we have that v t 2 = ac∙r . And now we just take the square roots. This is going to be the square roots of our centripetal acceleration, which is 0.0026, and then our radius, which is 3.85 × 10 8 meters . If you go ahead and work this out, you're going to get about exactly 1,000 meters 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 going to find. It's about 1000 meters per second as it travels around the Earth. Alright? So, that's it for this one, guys.