# Uniform Circular Motion

Now we examine uniform

circular motion. In uniform circular motion,

part of our definition is that the object moves

in a circular path. Now mathematically, that means

that our radius is constant. So if I place my

coordinate of my origin– my origin of my coordinate

system there at the center, then every place along that

path has the same value for r. And we used just a regular

r to represent that radius. The object also has to

move at constant speed. So as it’s moving

around this circle, the actual speed it moves

with doesn’t change. And it could be moving

counterclockwise, or clockwise, around the

circle, doesn’t matter. You can still have

uniform circular motion if it moves at constant speed. Now, in terms of our

equations again, that speed is the magnitude

of the velocity. So we’re going to use

just the regular v to represent our speed now. Now if I want to find

out what that speed is, it goes once around that

circle in a set time period. So if I measure someplace

as my starting place, I want to go once

around, and that’s going to be the

circumference of the circle. And however much time it

takes to go once around. So I can measure the speed then

as 2 pi r, the circumference of the circle,

divided by the time it takes to go once around. And this time period, the time

it takes to go once around, is called just the plain period. So they shortened

down time period for once around the

circle to just period. And you can calculate the

period then by using 2 pi r, over the velocity. So if you’re given the

speed and the radius, you can find the period. If you’re given the

radius and the period, you can find the speed. Now before we move

on, we want to know that even though the

speed is not changing, the velocity does change,

because the direction of motion is changing. If I think about

my circle again, as I move around the circle,

over here on this edge, I might be moving upwards. Where now, I’m

moving to the left. By the time I get to

this side of the circle, I’m moving downwards,

and when I move over here to this side of the circle,

I’m now moving to the right. So the direction

of motion changes, even if I stay going

counterclockwise the entire time. So that direction, or

the velocity change, that velocity

vector is changing. And so that means there does

have to be an acceleration. So uniform circular motion

has a constant radius, a constant speed, but

the velocity is changing, and so there is an acceleration. That’s a brief introduction

to uniform circular motion. We’ll take a look at a couple

of very closely related concepts here soon.