Conservation Laws

Just as there is the conservation of motion for objects traveling in straight lines, there is also a conservation of motion for objects traveling along curved paths. This conservation of rotational motion is known as the conservation of angular momentum. An object which is traveling at a constant speed in a circle (compare this to a race car on a circular track) is shown in Figure 3. The angular momentum for this object is defined as the product of the object's mass, its velocity, and the radius of the circle. For example, a 2,200 lb (1000 kg) car traveling at 30 MPH (50 km/h) on a 2–mi-radius (3-km) track, a 4,400 lb (2000 kg) truck traveling at 30 MPH (50 km/h) on a 1–mi-radius (1.6 km) track, and a 2,22200 lb (1000 kg) car traveling at 60 MPH (97 km/h) on a 1–mi-radius (1.6-km) track will all have the same value of angular momentum. In addition, objects which are spinning, such as a top or an ice skater, have angular momentum which is defined by their mass, their shape, and the velocity at which they spin.

In the absence of external forces that tend to change an object's rotation, the angular momentum will be conserved. Close to Earth, gravity is uniform and will not tend to alter an object's rotation. Consequently, many instances of angular momentum conservation can be seen every day. When an ice skater goes from a slow spin with her arms stretched into a fast spin with her arms at her sides, we are witnessing the conservation of angular momentum. With arms stretched, the radius of the rotation circle is large and the rotation speed is small. With arms at her side, the radius of the rotation circle is now small and the speed must increase to keep the angular momentum constant.

An additional consequence of the conservation of angular momentum is that the rotation axis of a spinning object will tend to keep a constant orientation. For example, a spinning Frisbee thrown horizontally will tend to keep its horizontal orientation even if tapped from below. To test this, try throwing a Frisbee without spin and see how unstable it is. A spinning top remains vertical as long as it keeps spinning fast enough. Earth itself maintains a constant orientation of its spin axis due to the conservation of angular momentum.

As is the case for linear momentum, there has never been a violation of the law of conservation of angular momentum. This applies to all objects, large and small. In accordance with the Bohr model of subatomic particles, the electrons that surround the nucleus of the atom are found to possess angular momentum of only certain discrete values. Intermediate values are not found. Even with these constraints, the angular momentum is always conserved.