Question

Two small balls A and B each of mass m, are attched erighdly to the ends of a light rod of length d. The structure rotates about the perpendicular bisector of the rod at an angular speed `omega`. Calculate the angular momentum of the individual balls and of the system about the axis of rotation.

Answer 1

Consider the situation shown in ure. The velocity of the ball A with respect to the centre O is `v=(omegad)/2`. The angular momentum of the ball with respect to the axis is `L_1=mvrm((omegad)/2)(d/2)=1/4momegad^2`
The same is the angular momentum `L_2` of the second ball. The angular momentum of the systes is equal to sum of these two angular momenta i.e. `L=1/2m omegad^2`.