First slide

Moment of inertia

Question

Three rings each of mass M and radius R are arranged as shown in the figure. The moment of inertia of the system about YY' will be

Easy

A

$3 M R^{2}$
B

$\frac{3}{2} M R^{2}$
C

$5 M R^{2}$
D

$\frac{7}{2} M R^{2}$

Solution

MOI of system about $Y Y^{'} : I = I_{1} + I_{2} + I_{3}$
where I₁ = moment of inertia of ring about diameter,
$I_{2} = I_{3} = MI$ of inertia of ring about a tangent in a plane
$∴ I = \frac{1}{2} M R^{2} + \frac{3}{2} M R^{2} + \frac{3}{2} M R^{2} = \frac{7}{2} M R^{2}$

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