Question

Derive the expression for the kinetic energy of a rotating rigid body

Answer 1

Consider a rigid body which rotates about y-axis The body is made up of large number of particles of masses

m

1

m1,

m

2

m2,

m

3

m3 and so on. The mass

m

1

m1 is at a distance

r

1

r1 and the mass

m

2

m2 is at a distance

r

2

r2 from the axis of rotation and so on. When the body rotates, each particle of the body moves in its own circle of a particular radius centred on the axis.

Answer 2

We can obtain a general idea of the rotation of rigid bodies and compare it with real situations or we can consider some real bodies as nearly rigid to obtain our results.The necessity of deriving an expression of kinetic energy of a rotating rigid body before defining moment of inertia lies inside the idea of defining moment of inertia.

It means we first find the kinetic energy of a rotating rigid body and compare it with the kinetic energy of a particle in linear motion - where we can find the measure of mass of a rotating body called moment of inertia.