## Class Notes, Spring 2002

 Week of Jan 14 Feb 4 Mar 4 Apr 1 Phy 360 page Jan 21 Feb 11 Mar 18 Apr 15 Jan 28 Feb 18 Mar 25 Apr 22 Feb 25

## Phy 360, Week 3

28 Jan Derive length contraction, as I hadn't done that before.

Show qualitatively how magnetic forces arise from electrical forces plus an understanding of simultaneity.

State without derivation the basic equations for energy and momentum

p = ( E / c2 ) v           E2 = p2 c2 + m2 c4

Explore some special cases, starting with the non-relativistic limit where v << c. In this case the momentum is small, so the p2c2 term is much smaller than the other, leading to the statement the the energy E is approximately mc2. Put this into the first equation and you find that the momentum is approximately mv.

The kinetic energy requires a bit more work to extract. You can eliminate p between the two equations, and get

E2 ( 1 - v2 / c2 ) = m2 c4

If v is not equal to c, then this is

E = m c2 / ( 1 - v2 / c2 )1 / 2

For small speeds, use the binomial expansion to get

E = m c2 + m v 2 / 2 + . . .

The kinetic energy is the difference between the total energy and the energy when at rest.

The other case, where v = c, implies that m = 0. Return to the original pair of equations and you have

E = p c

This is the energy-momentum relation for photons. Light carries momentum as well as energy even though it has zero mass.

30 Jan Applications of the mass-energy relations. Define the unit of energy the electron-Volt.

1 Feb Do one of the homework problems in some detail -- one involving the twin effect.

Set up the problem of solving for the proper acceleration, doing it the brute-force way, but not finishing it.

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