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)

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)
$=\frac{1}{2}MR^{2}+MR^{2}$
$=\frac{3}{2}MR^{2}$