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## Homework Statement

A ball of radius r

_{o}rolls on the inside of a track of radius R

_{o}. If the ball starts from rest at the vertical edge of the track, what will be its speed when it reaches the lowest point of the track, rolling without slipping?

Included below is a link to the diagram:

http://s3.amazonaws.com/answer-board-image/0c73c3d19aaa1d4c316cd2e6d2da8e57.jpg

## Homework Equations

v=R

_{o}ω

E

_{o}=mgh

E=0.5mv

^{2}+ 0.5Iω

^{2}+ mgh

I = (2/5)M(r

_{o})

^{2}

ω=Δθ/Δt

## The Attempt at a Solution

I've tried using conservation of energy to say that ƩE

_{o}=ƩE

So:

mgh= 0.5mv

^{2}+ 0.5Iω

^{2}+ mgh

which, when you plug in the moment of inertia for a sphere and the definition of ω:

mgh= 0.5mv

^{2}+ 0.5(2/5)M(r

_{o})

^{2})(Δθ/Δt)

^{2}+ mgh

These are my main problems:

1) How do I find a value for h? I understand that from the diagram, h is the distance from the end of the ramp to the ground but how I find a value for that?

2) How do I find time (which is needed to calculate ω)?

The final answer is supposed to be √(10/7)g(R

_{o}-r

_{o})

Thanks for any help!