## Friday, January 15, 2016

### Moment of Inertia in Rotational Motion Compared with Mass

Moment of inertia is a physical quantities which measures how easy it is or how difficult it is to put a body in rotational motion. Moment of inertia is the sum of  product of mass of each particle with square of distance from the axis of rotation. Mass is a physical quantity which explains the content of the body. It measures how easy it is or how difficult in it is to put a body in translatory motion.

Similarly to know how difficult it is to put a body in rotational dynamics, we shall study moment of inertia. If moment of inertia is small then it is easy to put a body in rotational motion and vice versa. To put a body in translatory motion, we shall overcome inertia of the body and to overcome that we need to apply force.

Similarly, to put a body in rotational motion, we need to overcome moment of inertia and to do that apply torque. It is not only the mass but the distance of the particles from the axis of rotation to know how difficult it is to put a body in rotational motion. For example if we take one kilogram of cotton and one kilogram of iron, it is easy to rotate iron about the axis when compared with cotton. It is just because size of iron is small when compared with cotton. Iron occupies small space and hence it has less moment of inertia. As moment of inertia is small it is easy to move iron body when compared with cotton body of same dimensions.

We can also apply a concept of radius of gyration to understand rotational dynamics. Radius of gyration is the effective distance of the body from the axis of rotation. We can also express moment of inertia in terms of radius of  gyration.

It is explained in detail in the following video lesson.

Change of Moment of Inertia with Axis of Rotation

Moment of inertia of a body depends on the size of the body, shape of the body, mass of the body and the distance of the particles from axis of rotation. All this distances are measured from axis of rotation. When ever the body axis of rotation is changed, the distance of the particles from axis of rotation also changes. Hence moment of inertia also changes.

It is further explained in detail in the following video lesson.

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