Question

Which has a larger moment of inertia, a disc of mass 61 kg or a hoop of mass 36 kg with the same radius

Answer 1

Answer:

The ring has a larger moment of inertia.

Explanation:

Given that the mass of disc=61 kg

Let the radius of the disc is R

The moment of inertia of the disc having mass m, about the axis passing through the center of the disc,

$I_{disc} = \frac {mR^2}{2}=\frac {61R^2}{2}=30.5 R^2$

Mass of hoop = 36 kg

As the radius of disc and hoop is the same, so the radius of the hoop is R.

The moment of inertia of the ring (hoop) having mass m, about the axis passing through the center of the disc,

$I_{hoop} = mR^2=36 R^2$

Hence, the ring has a larger moment of inertia.