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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?

(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?

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