It has been established since long that a rigid body is composed of small particles. If the mass of every particle of a body is multiplied by the square of its perpendicular distance from a fixed line, then the sum of these quantities (for the whole body) is known as **mass moment of inertia** of the body. It is denoted by I.

Consider a body of total mass m. Let it be composed of small particles of masses m1, m2, m3, m4, etc. If k1, k2, k3, k4, etc., are the distances from a fixed line, as shown in Fig. 1.4, then the mass moment of inertia of the whole body is given by

I = m1 (k1)2 + m2 (k2)2 + m3 (k3)2 + m4 (k4)2 + ….

If the total mass of a body may be assumed to concentrate at one point (known as centre of mass or centre of gravity), at a distance k from the given axis, such that

mk2 = m1 (k1)2 + m2 (k2)2 + m3 (k3)2 + m4 (k4)2 + …..

then——————————————————————- I = m k

*The distance k is called the radius of gyration. It may be defined as the distance, from a given reference, where the whole mass of body is assumed to be concentrated to give the same value of I. *

The unit of mass moment of inertia in S.I. units is kg-m2.

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