Uniform Circular Motion

# 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.