Answer to Question #287309 in Mechanics | Relativity for Ume

Question

Derive the momentum of inertia component of a rotating rigid body

Answer 1

Assume we have a point mass m rotating at distance r from the axis of rotation at speed v. Then, by definition, the moment of inertia is

$$I=\dfrac L\omega=\dfrac {[mv·r]}{[v/r]}=mr^2.$$