Even when angular momentum is not a very intuitive quantity, many situations in physics can better be understood based on it. In particular, when the angular momentum is conserved. Just as the linear momentum was defined based on Newton's second law of motion (constant mass, ),
where is the linear momentum the angular momentum is defined from the effect of torques in the motion of an object.
When the net torque acting on a particle is zero the angular momentum is conserved (or unchanged with time).
Thus, correspond to or and
From the diagram, . Calculating the relation between the velocities with respect to the two selected points by taking the derivative with respect to the time, , but implying and the velocity and linear momentum are unchanged by this shifting of the selected point.
On the other side, the angular momentum changes with this transformation to
In the previous expression, the angular momentum can be the same only when . Also, in the special case that , the angular momentum calculated from point is zero, , even when the angular momentum with respect to point is not zero.