Question

The kinetic energy of a rotating body depend upon:
A. Distribution of mass only
B. Angular speed only
C. Distribution of mass and angular speed
D. Angular acceleration only

Answer 1

Hint: The kinetic energy of rotation is proportional to the moment of inertia of the body and the square of the angular speed of the body.

Complete step by step solution:
Kinetic energy of a rotating body is given by
\[K=\dfrac{1}{2}I{{\omega }^{2}}\]
Where I denote the moment of inertia of the body about the axis of rotation and \[\omega \] denotes the angular speed.
The mass of a body is a measure of its inertia.
So, kinetic energy of the body depends on distribution of mass (inertia) and angular speed.

Therefore, option C. is the correct answer.

Additional information:
The kinetic energy of linear motion of a body is equal to half the product of mass of the body and square of the linear velocity of the body.
The property of a body by virtue of which it opposes any change in its state of rotation about an axis is called the moment of inertia of the body about that axis.
The angular velocity of all the particles of the rotating body will be the same but their linear velocities will be different.

Assuming that the body is made up of a large number of minute particles, each particle is at an unequal distance from the axis of rotation. Then the moment of inertia of the whole body about the axis of rotation will be equal to the sum of the moments of inertia of all the particles.

Note: As the particle of the rotating body is at unequal distance from the axis of rotation, so moment of inertia of the body is taken into consideration for determining the kinetic energy.