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Q.
The moment of inertia of a rigid body, depends upon:
AFMCAFMC 2002
Solution:
Let there be a rigid body of mass $M$. Let the body be made up of a large number of minute particles with masses $m_{1}, m_{2}, m_{3}, \ldots \ldots \ldots$, and $r_{1}, r_{2}, r_{3}, \ldots$ be their respective distances from the axis of rotation.
Then their moments of inertia are
$m_{1} r_{1}^{2}, m_{2} r_{2}^{2}, m_{3} r_{3}^{2}, \ldots \ldots$
The moment of inertia of the whole body about the axis of rotation will be
$I=m_{1} r_{1}^{2}+m_{2} r_{2}^{2}+m_{3} r_{3}^{3}+\ldots \ldots$
or $I=\Sigma m r^{2}$
Hence, moment of inertia depends upon the distribution of mass from axis of rotation.
