# Non-uniform Circular Motion

Now we can look at

non-uniform circular motion. Remember in uniform

circular motion, we had that the object

moves in a circular path. And that means that my radius

is constant all the way around the circle. But we also have that the

object moves at constant speed. So my v is constant

everywhere around the circle. For non-uniform

circular motion, I still have the object moves

in a circular path with a constant radius. But now the object moves

at a variable speed. So my v is changing at different

points around the circle. Now, there’s a lot

of different ways that the speed could change. It could be speeding up,

like the example I just showed where at every

point around the circle it’s going a little bit

faster than it was before. You could also

have slowing down. That might happen if you’ve

got friction somehow involved in the system. Another common one is to have

it slower at the top and faster at the bottom. So this will happen

when you’ve got gravity involved in some sort

of vertical circular motion. Now, we’ve got

accelerations involved here. Because I’ve got a

changing speed that means I’ve got a tangential

acceleration. And because it’s

circular motion, I’ve got a changing direction. So that means I’ve got

a radial acceleration. And for circular

motion we can refer to our centripetal acceleration

in terms of a specific equation for that radial acceleration. So that leads us to

our force equations. We want to use two components. But instead of

using x and y, I’m using my tangential component

and my radial component. In this case I’ve left my

tangential acceleration is just at, but for my

radial acceleration I went in and had

put the negative for inward and my

centripetal acceleration. And as always with

your force equations, you’re going to

have to figure out which physical forces

are in the tangential and the radial directions. And a physical force might have

components in each of those. But more than that, we

also have to recognize that it’s going to be

different at each point around the circle. If nothing else, your

velocity is changing as you’re going around. And so that’s going

to cause you to have different amounts

of radial forces at each point around the circle. Also you could have a

difference in exactly which physical forces

are in which direction at any particular point

around the circle. So you can find the specifics

for a specific moment as it’s going around the circle. But you still have to take into

account all the other factors and all the other places

around the circle. So that’s our non-uniform

circular motion.