Motion of Rotation:

The principle of conservation of energy is also useful in solving out problems involving motion of rotation. The mass moment of inertia I_m of a body of mass M with radius of gyration (r_k) for rotation about KK axis is given by (M (r_k) 2 and KE of rotation is (I _m ω² /2), where ω is the angular velocity in rad/sec of the body around the axis KK.

 (i) In case of solid cylinder or disk of mass (M) and radius (a) M. I. around centroidal axis,

I _m = M a ² / 2

 (ii) In case of a bar of length (L) and mass uniformly distributed along its length rotating about its centroidal axis,

I _m = M L² /12

If the above referred bar AB of length (L) is rotating about its end A or B,

I _m = M L² /12 + M (L/2)² =ML²/3

The general expression for moment of inertia of a body may be obtained as explained in units of centre of gravity and moment of inertia.