A shorter proof is obtained by using the relation of angular momentum to angular velocity, L = m r 2 ω ω , which holds for a particle traveling in a plane perpendicular to L . Specifying to inverse-square central forces, the time derivative of p × × L is d d t p × × L = ( − − k r 2 r ^ ^ ) × × ( m r 2 ω ω ) = m k ω ω × × r ^ ^ = m k d d t r ^ ^ , where the last equality holds because a unit vector can only change by rotation, and ω ω × × r ^ ^ is the orbital velocity of the rotating vector. Thus, A is seen to be a difference of two vectors with equal time derivatives.