The rotational analogue of linear momentum is angular momentum,
L. After torque and
equilibrium, angular momentum is the aspect of rotational motion most likely to
be tested on
Physics. For the test, you will probably have to deal only
with the angular momentum of a particle or body moving in a circular trajectory.
In such a case, we can define angular momentum in terms of moment of inertia and
angular velocity, just as we can define linear momentum in terms of mass and
L = l?
The angular momentum vector always points in the same direction as the angular
Angular Momentum of a Single Particle
Let’s take the example of a tetherball of mass
m swinging about on a rope of length
The tetherball has a moment of inertia of I =
mr2 and an angular velocity of
= v/r. Substituting these values
into the formula for linear momentum we get:
This is the value we would expect from the cross product definition we saw
earlier of angular momentum. The momentum, p
= mv of a particle moving in
a circle is always tangent to the circle and perpendicular to the radius.
Therefore, when a particle is moving in a circle,
L = pr sin90° = pr = mvr