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

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) (1/2) MR2 ω  (B) (3/2) MR2 ω  (C)  MR2 ω  (D)  2 MR2 ω

Tardigrade Admin · Accepted Answer

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 = M R^{2} ω + I \cdot ω

Here,

I = \frac{M R ^{2}}{2}

(for disc) and

ω =

angular velocity of the rigid body

= M R^{2} ω + (\frac{M R ^{2}}{2}) ω

= \frac{3}{2} M R^{2} ω

Q. 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

$\frac{1}{2} M R^{2} ω$

$\frac{3}{2} M R^{2} ω$

$M R^{2} ω$

$2 M R^{2} ω$

Q. 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

21​MR2ω

23​MR2ω

MR2ω

2MR2ω

$\frac{1}{2} M R^{2} ω$

$\frac{3}{2} M R^{2} ω$

$M R^{2} ω$

$2 M R^{2} ω$