Law of conservation of angular momentum

Explanation

Law of conservation of angular momentum : It states that the angular momentum of a rotating body is conserved if the resultant extanal torque on the body is zero.
Explanation: Consider a particle of mass m rotating about an axis with torque `tau`Let `vecP` be the linear momentum of the particle of mass m and `vec r` be its positio vector.
By definition, angular momentum is given by
`vecL=vecr xx vecp " " `...(i)
On differentiating equation (i) w.r.t. time t, we get
`(d vecL)/(dt)=(d)/(dt)(vecr xx vecP)`
`(d vecL)/(dt)=vecr (d vecp)/(dt)+vecp (d vecr)/(dt)`
But `(d vecr)/(dt)=vecv, (d vecp)/(dt)=vecF and vecp=m vec v`
`(d vecL)/(dt)=vec r xx vecF +m(vec v xx vecv)`
`=vec r xx vec F" " [because vecv xx vec v = v^(2) sin 0^(@) =0]`
`(d vecL)/(dt)=vecr xx vecF`
`(d vecL)/(dt)=vec tau`
If, `vec tau =0`
`(d vec L)/(dt)=0`
`therefore L=` constant.