Problem # p048

Moment of Inertia, Rigid Body
The polar mass moment of inertia of a slender rod of length L and mass m with respect to its center of mass is given by the equation :

  1. Use this equation and the parallel axis theorem to find the expession for the polar moment of inertia with respect to the end point of the rod. Show all of your work.

  2. Derive the same equation by the method of integration starting with the definition :
    where r is the distance of a mass-element dm from the end of the rod. Clearly define your choice for dm.