Question

Find the ratio of the magnitude of the angular momentum of a rolling disc about origin to that about the point P on the disc, as shown in the figure.

Answer 1

Given: A disc of mass M and radius R is rolling with angular speed w on a horizontal plane as shown.

To find the ratio of the magnitude of the angular momentum of a rolling disc about origin to that about the point P on the disc,

Solution:

angular momentum of a rolling disc about origin,

${\omega }_1=m{R}^{2}w$

angular momentum of a rolling disc about the point P on the disc,

${\omega }_2=m\frac{R^2}{2}w$ (as the distance between center and point P is $\frac{R}{2}$)

so the ratio of the magnitude of the angular momentum of a rolling disc about origin to that about the point P on the disc is

${\omega }_1:{\omega }_2=m{R}^{2}w:m\frac{R^2}{2}w⟹{\omega }_1:{\omega }_2=2:1$

is the required ratio