# Centrifical Motion Theoretical Question

1. Jan 4, 2012

### Retricide

1. The problem statement, all variables and given/known data
A ball of unknown mass is attached to a massless string. The string is then held at the opposite end and the ball is pushed, as to give it a centrifical motion (acceleration toward the center and perpendicular velocity). NOTE: The length of the string is not the radius (the string is the hypotenuse) and all angles are unknown.
The ball swings around a circle, of known radius, and period of rotation is measured 10 times and then divided by 10 to get an average period. The radius of the circle (R), length of the string (L), and period of ball (T) are known.

Derive an equation relating the period of the ball (T) to the length of the string (L) and radius of the circle (R).
There should be no angles in your final equation, since you will not be directly measuring angle.

I think you are allowed to use Ft (tension) in the equation (mass as well, but I think it should cancel out).

2. Relevant equations
Fnet=ma
a(centripetal)=(4∏^2R)/T^2

3. The attempt at a solution
Ft is in a different plane than acceleration, so I resolved Ft into component x and y vectors.
I solved Fty to equal mg
and Ftx to equal (m4∏^2R)/T^2.

However, I'm not sure where to go from here and how to incorporate L into the equation.
I know I can use arccos to get an angle from L and R, which would incorporate L into the equation, but that would mean I have an angle (arccos) in my equation, which, I cannot have.

Any ideas how to incorporate L into the equation relating T and R?

Last edited: Jan 4, 2012
2. Jan 4, 2012

### Retricide

Oh, I think I've got it actually.

I forgot to break Fty down into
Ftsin(arccos(L/r))=mg

Problem solved :3