Question

A circle disc of mass 'm' and radius 'R' is set into motion on a horizontal with a local speed V in the forward direction and an angular speed $W=\frac{V}{r}$ in clockwise direction as shown in fig find the magnitude of the total angular momentum of the disc about the bottom-most part 'o' of the disc:

Answer 1

Given,

Angular velocity of disc, $\omega =\frac{v}{r}$

Inertia of disc, $I=\frac{1}{2}m{R}^2$

Angular momentum, $\overrightarrow{L}=I\omega =\frac{1}{2}m{R}^2\frac{v}{R}=\frac{mRv}{2}$

Angular momentum is $\frac{mRv}{2}$