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**1. The problem statement, all variables and given/known data**

Two particles A and B having equal masses m are rotating around a fixed point O with constant angular speed ω .A is connected to point O with a string of length L/2 whereas B is connected to point A with string of length L/2 .Find the angular momentum of B with respect to A about O.

O-------L/2-------A-------L/2--------B

**2. Relevant equations**

**3. The attempt at a solution**

There can be two approaches

1.We find angular momentum of B w.r.t O ,say L1 = mω

^{2}L.Then we find angular momentum of A w.r.t O ,say L2 = (mω

^{2}L)/4.Since angular momentum is a vector , angular momentum of B w.r.t A should be vector difference of L1 and L2 =(3/4)(mω

^{2}L)

2.We find relative velocity of B w.r.t A =ωL/2 ,i.e we have considered particle A to be at rest .Then we find shortest distance between point A and line of motion of B which is L/2 .

Now,angular momentum of A w.r.t B =(mω

^{2}L)/4

I feel approach 1 is the correct way of calculating angular momentum of a point with respect to a moving point ,but the correct answer is the one given by approach 2.

Which is the right way ?