Angular Momentum and
Rotational Velocity
For the simple case of a small mass executing uniform
circular motion around a much larger
mass, the amount of
angular momentum takes a simple form. As the adjacent figure illustrates, the
magnitude of the angular momentum in this case is L = mvr, where
L is the
angular momentum, m is the mass of the small object,
v is the magnitude of its
velocity, and r is the separation between the
objects.
Because the above formula
can be rearranged to give v = L/(mr) and L
is a constant for an isolated
system, the velocity v and the separation r
are inversely correlated. Thus a decrease in the separation
r is accompanied by an increase in the velocity v,
and vice versa.