Question:
Why does a solid sphere have a smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?
Solution:
The moment of inertia is directly proportional to the square of the distance of the mass from the axis of the rotation. In a solid sphere, the distribution of mass takes place
from the centre to the radius of the sphere. Whereas in a hollow cylinder, the mass is concentrated on the peripheral surface. Therefore, the moment of inertia of the
hollow cylinder is more than the moment of inertia of the cylinder.
$I=\sum_{i=1}^{n} m_{i} r_{i}^{2}$
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