Question 9.8: Moment of inertia of a hoop Find the moment of inertia of a ...
Moment of inertia of a hoop
Find the moment of inertia of a uniform hoop of mass M and radius a about its axis of rotational symmetry.
This is the easiest case to treat since each particle of the hoop has perpendicular distance a from the specified axis. The required moment of inertia is therefore
I=\sum\limits_{i=1}^{N} m_{i} a^{2}=\left(\sum\limits_{i=1}^{N} m_{i}\right) a^{2}=M a^{2},
where M is the mass of the whole hoop.
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