Question

A disc of mass M and radius R is rolling with angular speed w on a horizontal plane as shown in figure. The magnitude of the angular momentum of the disc about the origin O is

• A. $\frac{1}{2} MR^2 \omega $
• B. $\frac{3}{2} MR^2 \omega $
• C. $ MR^2 \omega $
• D. $ 2 MR^2 \omega $

Answer 1

Answer: (B)

Here, disc has two types of motion namely translational and rotational. Hence, angular moment of a rigid body in translational cum rotational
$=$ angular momentum of centre of mass about origin $(O) +$ angular momentum of the body about centre of mass.
$\Rightarrow L =MR^{2} \omega + I \cdot\omega $
Here, $I = \frac{MR^{2}}{2}$ (for disc) and $\omega =$ angular velocity of the rigid body
$= MR^{2} \omega + \left(\frac{MR^{2}}{2}\right)\omega $
$ = \frac{3}{2}MR^{2}\omega$