While playing a game of skeeball, at a carnival, you have your option of using o

Question

While playing a game of skeeball, at a carnival, you have your option of using one of two otherwise identical balls of a mass (m) and radius (r). The first ball is solid, while the second is hollow. A.) If they are both rolled without slipping up a frictionless ramp at the same initial velocity(v), which ball reaches the greater height and why? B.) when they roll back to the bottom of the ramp (again without slipping) which ball will have the greater linear momentum and why? C.) which will have the greater angular momentum and why?

Explanation / Answer

A) Hollow ball will reach to a greater height because of its initial rotation kinetic energy is more as its moment of inertia is more.

B) They both will have same linear momentum. It is because in both cases, the final velocity will be equal to intial velocity and we know initially they had been given equal initial velocity.

C) hollow sphere will have larger angular momentum. This is because angular velocity(w=v/r) is same, and hollow sphere has larger moment of inertia(I), and angular momentum = Iw

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