Question

A circular disc of mass M and radius R is rolling on a horizontal surface with an angular speed $\infty$. The magnitude of angular momentum of the disc about the origin 'O is'

• A. ${MR}^2\infty$
• B. $\frac{M{R}^2\infty }{2}$
• C. $\frac{3}{4}{MR}^2\infty$
• D. $\frac{3}{2}{MR}^2\infty$

Answer 1

The correct option is D $\frac{3}{2}{MR}^2\infty$

$\omega =\frac{v}{R}$ (rolling)

Angular momentum about origin $=mv{r}_{\perp }+I_o\omega$

$v_{\perp }=$ distance perpendicular to velocity from origin

$I_o=$ Moment of inertia about point O (centre of mass of disk)

$=m\frac{\omega R}{1}\times R+\frac{m{R}^2}{2}\omega$

$\Rightarrow \frac{3m{R}^2\omega }{2}$ $(\omega =\infty )$

$=\frac{3m{R}^2\infty }{2}$.