D-3 ANGULAR MOMENTUM IN INELASTIC COLLISIONS

1. PURPOSE:

To study conservation of energy and momentum in a two-dimensional inelastic collision.

2. APPARATUS:

Air table, camera, film, pucks, rubber or plastic collars, Velcro collars, vacuum cleaner air source, and connecting hoses.

3. REFERENCES:

1. Experiment D-2, and the references listed there.

4. GENERAL METHOD:

The collision is arranged as in experiment D-2, but the moving puck is aimed off-center of the stationary one to ensure a truly two-dimensional collision.

5. THEORY:

Fig. 1. Angular momentum definition.

The angular momentum of a point mass about an axis is P×R where R is the vector from the axis to the mass, and P = mv is the linear momentum of m. From the definition of cross product, and Fig. 1, prove that the size of the angular momentum is also given by mvL, where L is the perpendicular distance from the axis C to the line of action of the force. (Compare the definition of torque.) L is called the impact parameter.

6. PROCEDURE:

(1) Investigate a partially elastic collision, using rubber or plastic collars on one or both pucks.

(2) Investigate a perfectly inelastic collision, using Velcro collars on both pucks. Velcro is a material with many tiny plastic hooks. When two pieces of Velcro are pushed together, the hooks engage, and the pieces are difficult to separate. This material is often used in clothing in place of buttons or zippers.

7. ANALYSIS:

Verify to what extent energy, linear momentum, and angular momentum are conserved in this experiment.

Remember that the conservation of linear and angular momentum are two different, independent conservation laws, but there is only one law of energy conservation. Linear and angular kinetic energy represent different terms in one energy equation.