Starting from the definition of angular momentum in terms of position vector and linear momentum vectors. S.T. the time derivative of angular momentum is equal to the torque acting on the particle.

Explanation

We know that `vecL=vecrxxvecP`
Differentiating both sides, we get
`(dvecL)/(dt)=d/(dt)(vecrxxvecp)` i.e. `(dvecL)/(dt)=(dvecr)/(dt)xxvecp+vecrxx(dvecp)/(dt)`
but `vecv=(dvecr)/(dt)` and `vecp=mvecv` i.e. `(dvecL)/(dt)=vecvxxmvecv+vecrxx(dvecp)/(dt)` where `vecvxxvecv=0`
Hence `(dvecL)/(dt)=vecrxx(dvecp)(dt)` where `(dvecp)/(dt)=vecF`
where `vecrxxvecF=vectau" ":.(dvecL)/(dt)=vectau`