Question

50 point question!

A hollow sphere and a solid sphere of the same mass and radius are spinning with the same angular velocity. Which sphere has the greater angular momentum?

A) The solid sphere
B) The hollow sphere
C) Both
D) Impossible to tell

Please explain your answer, too. Thanks!

Answer 1

The moment of inertia denoted by I(it tells how much mass is distributed about axis, here it is that axis about which objects/bodies are rotating) of solid sphere is greater than that of hollow sphere.

Angular momentum of solid sphere(L₁) = I₁ω------ 1.
Angular momentum of hollow sphere(L₂) = I₂ω.------2.

Divide 1 and 2,
L₁/L₂ = I₁/I₂
∴L₁ = L₂(I₁/I₂).

Since I₁>I₂,
L₁>L₂
Therefore angular momentum of solid sphere will be greater

Answer 2

The hollow sphere would have a higher moment of inertia because more of the mass is situated farther from the center of mass. Since the rotational speeds are the same, the hollow sphere would have a higher rotational momentum.