Show that the angular momentum about any point of a single particle moving with constant velocity remains constant throughout the motion.

Explanation

Suppose the particle with velocity `vecv` be at point P at some instant t. We have to calculate the angular momentum of the particle about point O.
The angular momentum is `vecl=vecrxxmvecv` and its magnitude is `l=mvr sin theta` where `theta` is the angle between `vecr and vecv`.
Its position changes with time, but line of direction of `vecv` remains the same and hence `OM=rsintheta` is a constant.
Further, the direction of l is perpendicular to the plane of `vecr and vecv`.
It is into the page of the figure. This direction does not change with time.
Thus, `vecl` remains the same in magnitude and direction and is therefore conserved.
Hence `v_(0)` external torque actin g on particle.