Problem # p047

Moment of Inertia, Rigid Body

The mass moment of inertia of a circular plate about the axis going through its center perpendicular to the plate is given by :

    = 1/2 m R2

where m=mass of plate, R=radius of plate.

Derive this equation using the definition of the moment of inertia :

where r is the distance of a small mass-element "dm" from the center of mass of the plate. For "dm" you might want to take the mass of thin concentric rings of width dr. Give the equation defining your "dm".