Question

What is the difference between orbital velocity and radius AND is this different to the relationship between velocity and radius in the centripetal force equation. If so how?

Answer 1

Depends on the orbit.

If you have a circular orbit, then that it obviously circular motion and centripetal force equations would apply.

If your orbit has an eccentricity other than 0, then you'll need to modify your geometry appropriately. Your satellite will not be orbiting at a constant distance.

Answer 2

I'm actually asking because I'm doing an experiment in which I have to investigate the relationship between orbital velocity and radius. I'm doing so by using a ball on a string. I'm at a loss as to what I'm supposed to be looking for in my results

Answer 3

Okay, well if your swinging the ball over your head, then your assumption will be circular motion as the string is a finite length. So your centripetal equations should apply.

F = m v^2 / r
a = m v / r

Answer 4

Thanks. So within those equations, what is the relationship between r and v? I don't know how to graph my results...sorry if I'm not making sense. I think I've over-thought this to the point of delirium

Answer 5

here are my results

Answer 6

Okay, so you'll need to find a way to derive an expression that incorporates the period of revolution.

Period is the time to do 1 revolution:
So, that would be T = t/20, since you had it spin 20 times.

Then you can rewrite velocity as the circumference of the circular path divided by this period to get the orbital speed:

v = 2*pi*radius / T