Question

Consider the moment of inertia of a solid uniform disk, versus that of a solid sphere, about their respective centers of mass. Assume that they both have the same mass and outer radius, that they have uniform mass distributions, and that the disk is rotated about an axis perpendicular to its face. What is the relation between the moment of inertia of the disk Idisk and that of the sphere Isphere?

Answer 1

Answer:

$I_S=\dfrac{4}{5}I_D$

Explanation:

Given that

Both have same mass = m

The outer radius = R

The moment of inertia of disk

$I_D=\dfrac{mR^2}{2}$             -------1

The moment of inertia of solid sphere

$I_S=\dfrac{2mR^2}{5}$              -----------2

Now from equation 1 and 2

$I_S=\dfrac{2\times 2 I_D}{5}$      

$I_S=\dfrac{4I_D}{5}$      

$I_S=\dfrac{4}{5}I_D$

So we can say that moment of inertia of the sphere is less as compare to the disk for same mass and the for same outer radius.