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

Explanation

Let the particle with velocity v be at point P at some instant t. We want to calculate the angular momentum of the particle about an arbitrary point O.

The angular momentum is `l = r × mv`. Its magnitude is `mvr sin θ` , where `θ` is the angle between r and v as shown in Fig. 7.19. Although the particle changes position with time, the line of direction of v remains the same and hence `OM = r sin θ` . is a constant.
Further, the direction of l is perpendicular to the plane of r and v. It is into the page of the figure.This direction does not change with time.
Thus, l remains the same in magnitude and direction and is therefore conserved. Is there any external torque on the particle?