Two particles of mass m each are attached to a light rod of length d, one at its centre and the other at a free end, The rod is fixed at the other end and is rotated in a plane at an angular speed `omega`. Calculate the angular momentum of the particle at the end with respect to the particle at the centre

Explanation

The situation is shown in ure. The velocity of the particle with respect to the fixed end O is `v_A=omega(d/2)` and that of B with respect to O is `v_B=omegad`. Hence the velocity of B with respect to A is `v_B-v_A=omega(d/2). `the angular momentum of B with respect to A is therefore
`L=mvr=momega(d/2)=1/4momegad^2`
along the directiion perpendicular to the plane of rotation.