Question

A solid cylinder of mass $M$ and radius $R$ rolls on a flat surface. Find its moment of inertia about the line of contact.

• A. $\left(\frac{3}{2}\right)M{R}^2$
• B. $M{R}^2$
• C. $2M{R}^2$
• D. $\left(\frac{2}{3}\right)M{R}^2$

Answer 1

Answer: (A)

Moment of inertia of solid cylinder about $O$,
$I_{CM}=\frac{1}{2}M{R}^2$
Moment of inertia about point of contact $P$,
$I_p=I_{CM}+M{R}^2$ (using parallel axes theorem)
$=\frac{1}{2}M{R}^2+M{R}^2$
$=\frac{3}{2}M{R}^2$