# How to find angular momentum about other axes?

Two particles each of mass m are attached by a light rod (massless and cannot bend or stretch) of length l. A particle "A" of same mass strikes B. The collision is perfectly elastic. Find angular momentum of the rod system. There are no other external forces.

Now I have done this by conserving angular momentum about a fixed axis in-line to the center of mass (just beside it, fixed to the ground) so angular velocity of COM about that axis becomes zero. I imagined the rod system rotating about the COM with COM itself translating forward.

Now suppose I wanted to find the required answer by conserving angular momentum NOT about an axis about which angular velocity of COM is zero, but the angular velocity of particle C is zero.

I have tried by taking a fixed axis beside C. But even from that axis, the angular momentum comes to be :

L = Iw + Mvr

where I is momentum of inertia about COM, w is angular velocity about it, Mv is linear momentum of COM and r is perpendicular distance from axis, here r = l/2

Is there is such an axis (fixed to the ground) about which I can assume angular velocity of C to be zero? If yes, then how can I find angular momentum?

• If this collision is elastic, the the rebound motion of particle A must be considered when calculating the final angular momentum. Once mass C is moving it will have an instantaneous angular velocity (and corresponding angular momentum) relative to any fixed axis which is not in-line with its velocity vector. Jan 4, 2021 at 21:36