Rotational motion

Rotational motion

Rotational motion

Some important definitions 

Rotational motion: - 

The motion of object about its own axis is called rotational motion.

Rigid body: -

A rigid body is one whose geometric shape and size remain unchanged under the action of any external force.

Center of mass: - 

It is the point where whole mass of the body is supposed to be concentrated.

Moment of Inertia: - 

The moment of inertia of a rigid body about an axis of rotation is define as the sum of product of the mass of each particle and the square of its perpendicular distance from the axis of rotation.

Explanation:- Consider a rigid body rotating about an axis passing through any point ‘O’ in anticlockwise direction.

Moment OF Inertia

Physical significance of moment of inertia :-

From the above table it is evident that moment of inertia plays the same role in rotational motion as mass in linear motion i.e. significance of the moment if inertia in rotational motion is similar to that of mass in linear motion. This is the physical significance of moment of inertia.

      In linear motion of a body mass represent inertia of a body i.e. tendency of a body to oppose any change in state of its linear motion.

      In rotational motion of a body moment of inertia represent inertia of a body i.e. tendency of a body to oppose any change in the state of its rotational motion.

Radius of Gyration:- 

It is define as the distance between axis of rotation and the point where whole mass of the body is supposed to be concentrated so as to possess the same moment of inertia as that of the body. It is denoted by ‘K’.

Physical significance of radius of gyration:-

The radius of gyration ‘K’ of a body about an axis gives an idea about the distribution of mass of the body with respect to that axis. A large value of ‘K’ shows that the mass of the body is distributed widely about the axis so that moment of inertia  is large. A small value of ‘K’ shows that the mass is distributed closed to the axis so that the moments of inertia is small.