# Moment Of Inertia And Its Significance

**This article is about moment of inertia and its physical significance.**

**Moment of Inertia and its significance :**

According to newton's first law of motion the body continues to stay in the state of rest or in the state of motion. This property of inertia possessed by all the matter is the measures of mass in translatory motion. Similarly when a body is rotating or fixed about an axis. Any change in its state of rest or motion can be brought about by a couple or Torque the greater the opposition to change greater is the inertia. It is this rotational inertia of the body is called its moment of inertia about its axis of rotation.

The analogy between the two types of motion is the mass defined as " Coefficient of inertia for translatory motion" and the moment of inertia defined as "Coefficient of rotational inertia in rotating motion". In translatory motion the motion of the body depends on the mass alone.

In rotatory motion, the moment of inertia of the body depends not only on the mass of the body but also upon the effective distance of the body from the axis of rotation. The effective distance K of the particles from the axis of rotation is called the radius of gyration about that axis and is equal to root mean square distance of the particles from the axis.

"The radius of gyration of a body about a given axis of rotation is the distance from the axis of rotation is the distance from the axis at which if the whole mass of the body were to be concentrated, the moment of inertia of the body about the axis of rotation would be the same as with the actual distribution of mass.

The mass of body remains the same, irrespective of rotation, the value of radius of gyration about the axis depends upon.

a) The position and direction of the axis of rotation

b) The distribution of the mass of the body about this axis, the value for the same body is different at different inclination.

The radius of gyration of a body about a given axis of rotation given an inclination of the distribution of the mass of the body about it and hence the effect of distribution mass on the moment of inertia about that axis.

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