Circular Motion, and Conservation of Energy problem

[leighzer]

A ball of mass m is spun in a vertical circle having radius R. The ball has a speed v(o) at its highest point. Take zero potential energy at the lowest point, and use the angle theta measured with respect to the vertical.

(a) Derive an expression for the speed v at any time as a function of R, theta, v(o), and g.
(b) What minimum speed v(o) is required to keep the ball moving in a circle?


I found part (a) to be:

v = *square root*[ v(o)^2 + 2gRsin(theta) ]


I'm not totally sure if this is correct, and i don't know how to find the minimum value of v(o).


Is someone able to help?

 

[leighzer]

The only thing I can think of for part (b) is that v(o) must be greater than or equal to:

-*sqr rt*[ 2gRsin(theta) ]

in order to keep the value inside the square root of the first equation positive.