Non-uniform Circular Motion

# 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
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.