System Of Particles Rotational Motion

Key Idea : Kinetic energy of rotation is half the product of the moment of inertia (I) of the body and the square of the angular velocity of the body.
Kinetic energy of rotation moment of inertia angular velocity.
i.e.

Given,




From the equation of angular motion, we have

where is initial angular velocity,
is angular acceleration and is time.
Given,



Note : The equation of kinetic energy of rotation is similar to kinetic energy expression in linear form and equation of angular motion is similar to Newton's equation of motion

In rolling without slipping, total energy of ball is the sum of its translational and rotational energy.
Kinetic energy of rotation

where is radius of gyration.
Kinetic energy of translation,

Thus, total energy




Hence