Question

A thick ring has inner radius 1/2R, outer radius R, and mass M.

Find an expression for its rotational inertia.

Express your answer in terms of the variables R and M.

Answer 1

moment of inertial of solid ring = 0.5MR^2
moment of inertia of given ring = moment of inertia od solid ring - moment of inertia of missing part from the solid ring
=> 0.5*(MpiR^2/pi(R^2 - (R/2)^2)) *R^2 - 0.5(MpiR^2/pi(R^2 - (R/2)^2)) *(R/2)^2
=> 0.5*(MpiR^2/pi(R^2 - (R/2)^2)) 3R^2/4
=> 0.5*M*R^2