Conservation of angler momentum

Conservation of angular momentum:-

If external Torque(८)is zero total angular Momentum remains constant.
For a particular angular momentum
              J=r×p(in vector)----------------(1)
Now diff.   eq1 with respect to time
  dJ/dt=d/dt(r×p)
             =r dp/dt+p dr/dt
             =r×F +(mv)v.    {dp/dt=F, two
                                       Vector cross v×v=0}

            =r×F +0                                                 dJ/dt = Torque ( moment of force)    {r×F=Torque}         
           
If Torque=0
Then.   dJ/dt=0
            
         [  J = constant  ]
Torque is rate of change of angular momentum.