Question

A solid sphere and a solid cylinder , both uniform and having the same mass and radius, are released from rest at the same height on a ramp. If they roll down the ramp without slipping, which one will have the lower forward velocity at the bottom of the ramp?

a. The solid sphere
b. The solid cylinder
c. Both will have the same forward velocity

Answer 1

I (cylinder) = 1/2 M R^2

I (sphere) = 2/5 M R^2

The equation of motion shows

I * alpha = M g R sin theta = const

An increase in the moment of inertia will result in a smaller acceleration

The cylinder will have the smallest forward velocity because it will arrive at the bottom after the sphere