Question
A rigid body of moment of inertia I is rotating with uniform angular velocity ω about a given axis. Derive an expression for rotational kinetic energy of the body.
Solution
Consider a rigid body consisting of n particles rotating about an axis XY with uniform angular velocity 
.
Let r1, r2...........,rn be the distances of particles from the axis of rotation.
Different particles are at different distances from the axis of rotation, therefore, the magnitude of linear velocities of different particles will be different.
Consider ith particle of mass mi at a distance ri from the axis of rotation.
The linear speed of ith particle will be
Vi = ri ω
Therefore, kinetic energy of ith particle due to rotation about XY-axis is,
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Total kinetic energy of rotation of the rigid body about XY-axis is
This is the required rotational K.E of the body.
