## Illustration 11.4: **Angular
Momentum and Area**

Please wait for the animation to completely load.

One of the strangest ideas regarding angular momentum is that an object
moving in a straight line can have angular momentum. Angular momentum for a
particle is given by the cross product **L **= **r** × **p**.
Given this, we see that the origin matters for the calculation of angular
momentum for a particle.

In the absence of a net external torque acting on a system, a particle's angular momentum remains constant.
For this discussion, the particle is free, so angular momentum should be
conserved. Is there a different way to state the concept of angular
momentum conservation? There may be. Consider the statement, Does a
particle sweep out equal areas in equal times (with respect to **any** origin)?

Specifically, in this Illustration does a free particle moving in a straight line sweep out equal areas
in equal times?

Press "start" to begin the animation, and let the show
begin: A black dot will move freely from left to right. Different colors show the area
the particle sweeps out with respect to some fixed point (the origin). Do all the areas have the same size? Click within each area and see what will happen. Certainly from mathematical equations we know the
area of a triangle = width * height/2. All of the areas have the same height and the same width (= v_{x}*dt).

Note: Kepler's second law (see Chapter 12 on gravitation for more
details) states, during equal time intervals, the radius vector from the
sun to a planet sweeps out equal areas. What does this tell you about the
angular momentum of the planets?

Illustration authored by Fu-Kwun Hwang and Mario Belloniy.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system
developed at St. Olaf College.