Question

Two small balls of mass m each area attached to a light rod of length e, one at its centre and the other at a free end. The rod is fixed at the other end and is rotated in horizontal plane at an angular speed $\omega$ Calculate the angular momentum of the ball at the end with respect to the ball at the centre.

Answer 1

As shown in figure , Ball A is at the center and Ball B is at free end.

Angular Momentum $\overline{L}=I\times \omega$

For Ball 'A' ,

$I$ about point O , $I=m\frac{e^2}{4}$

$\therefore {\overline{L}}_A=\frac{m\omega e^2}{4}$ .......1

For Ball 'B" ,

$I$ about point O , $I=m{e}^2$

$\therefore {\overline{L}}_B=m\omega e^2$ .......2

Using Equations 1 and 2,

${\overline{L}}_{BA}={\overline{L}}_B-{\overline{L}}_A=\frac{3}{4}m\omega e^2$