Advanced General Physics 323/324

Classical Mechanics Unit CM3 Central Force Motion

Prerequisite: CM2

Overview: This unit covers the mechanics of central force motion: the motion of a "point" particle" in a potential which depends only upon the magnitude of its displacement from a central point, not upon its direction. Examples are the motion of a planet in the gracitational field of the sun and the motion of an electron in the electric field of a proton (the hydrogen atom). It is shown that the conservation of angular momentum reduces this 3 dimensional problem to a one dimensional radial motion problem. You may want to review some of the basic material on angular momentum in Chapt. 6 before starting this unit

Read:

D. Kleppner and R. Kolenkow, An Introduction to Mechanics (K&K) Chapt. 9 - Central Force Motion

Comment: K&K is well-written and abounds with instructive and appropriate examples. The problems at the ends of the chapters are in many cases quite difficult, however, an the assigned problems have been chosen with care. The solutions are on file: just ask an instructor if you wish to see them.

After completing this unit you should understand:

  1. The angular momentum of a particle.
  2. The angular momentum of a rigid body .
  3. Torque.
  4. Central force motion as a one body problem.
  5. General properties of central force motion, such as the confinement to a plane and energy and angular momentum conservation.
  6. Planetary motion.
  7. Kepler's Laws.

Problems:

Chapt. 9: Problems 2,5,8,9a,12a.


Back to the Physics 323/324 Home Page.