an object sliding down a frictionless incline. Rolling objects pick up speed more slowly because
only some of the kinetic energy they gain is converted into translational motion, while the rest is
converted into rotational motion.
Angular Momentum
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 SAT
II 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 velocity:
The angular momentum vector always points in the same direction as the angular velocity vector.
Angular Momentum of a Single Particle
Let’s take the example of a tetherball of mass m swinging about on a rope of length r:
The tetherball has a moment of inertia of I = mr^2 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,
Newton’s Second Law and Conservation of Angular Momentum
In the previous chapter, we saw that the net force acting on an object is equal to the rate of change
of the object’s momentum with time. Similarly, the net torque acting on an object is equal to the
rate of change of the object’s angular momentum with time:
If the net torque action on a rigid body is zero, then the angular momentum of the body is constant
or conserved. The law of conservation of angular momentum is another one of nature’s
beautiful properties, as well as a very useful means of solving problems. It is likely that angular