Question

All of the above objects have the same mass M, and the same radial distance R from the axis of rotation as shown. Which of these objects has the largest moment of inertia about the central axis? (Show work to explain why!)

Answer 1

for point mass,

I = MR²

for hoop

I = MR²

for disk

I = 1/2 MR²

for sphere

I = 2/5 MR²

for rod at end

I = MR² / 3

so,

hoop and point mass have the largest moment of inertia about given axis, MR²