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. $\left(\frac{3}{2}\right)MR^{2}$
• B. $MR^2$
• C. $2\,MR^2$
• D. $\left(\frac{2}{3}\right)MR^{2}$

Answer 1

Answer: (A)

$\left(\frac{3}{2}\right)MR^{2}$

Answer 2

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