Advanced General Physics 323/324

Classical Mechanics Unit R2 Relativistic Energy and Momentum

Prerequisite: R1

Overview: This unit decribes how special relativity forces us to modify our definitions of energy and momentum in order to have consistent pictures in different inertial frames. It also forces us to the conclusion that increasing the energy of a system increases its rest mass (inertia), giving the famous E=mc². The special case of massless particle (for example the photon), which has no rest mass and always travel at the speed of light, is also discussed.

Read:

D. Kleppner and R. Kolenkow, An Introduction to Mechanics (K&K) Chapt. 13 - Relativistic Energy and Momentum; Chapt. 14 - FourVectors and Relativistic Invariance.

Comment: Be sure you understand how to work with energies in eV (or keV or MeV), masses in eV/c², and momenta in eV/c.

After completing this unit you should understand:

1. The energy and momentum of a particle of rest mass m moving at velocity : p = γ m v, E =γ m c², where γ = 1/√(1-v²/c²) .
2. The energy and momentum of the photon are related by E = pc .
3. In general, for particles of non-zero rest mass, E² = (mc²)² + (pc)².
4. How energy and momentum are conserved in collisions or decays.

Problems:

Chapt. 13: Problems 1-8,11; Chapt. 14: Problems 1-5 .