Moment of inertia of a body, about a given axis, is defined as the property by virtue of which it is unable to change its state of rest or of uniform rotational motion without the help of external torque. Moment of inertia depends upon the mass of body and distribution of mass about the axis of rotation. Moment of Inertia of a body, about a given axis, is equal to the sum of the products of masses of all particles of the body and squares of their respective perpendicular distances from the axis of rotation. Unit of moment of inertia is kg m2 in SI system and g cm2 in CGS system.
Moment of inertia can be calculated for a particle, thin straight rod, ring, solid disc, annular disc, solid sphere, rectangular lamina, rectangular block, cylinder etc.
Radius of gyration is the perpendicular distance of a particular point from the axis of rotation at which, if the whole mass of the body were supposed to be concentrated, the moment of inertia would be the same as that with the actual distribution of mass. Radius of gyration of a body about a given axis is equal to the square root of the mean of the squares of distances of various particles of the body from the axis of rotation.
Two theorems used for the study of moment of inertia of different bodies are perpendicular axes theorem and parallel axis theorem.
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