Retired Physics Curriculum: Special Relativity
For the past few years, this the last unit I did with the kids in the AP class. (In the previous schedule, we also did a little bit of elecrostatics and circuits.) Obviously, this is not part of the AP curriculum, but once we were done with the official things, this was a fun way to end the year.
I really like the flow of Astronomy -> Gravity -> Relativity. It really shows how our understanding of the universe grew and how the concepts of time, space and motion developed. As weird as relativity is, it all starts with an innocent little proposition followed to its logical conclusion.
Even though there is a lot of math in this unit, I consider it more conceptual as I did not base things off of Lorentz transformations, which is the usual college approach. My last couple years I started to get into spacetime diagrams, but never really had time in class to do it with the kids, which is too bad.
As with the Astronomy unit, none of this material is on the AP exam.
Super brief discussion of Einstein's 1905 papers and gives the two postulates of special relativity.
Speed factor, Lorentz factor and units where c=1.
Discusses what it means for two events to be simultaneous, and shows how different reference frames measure different things. Also shows how this can imply length contraction. There is no math, but it does make your brain explode the first time you see this.
These are problems on the basic postulates of special relativity and simultaneity. No math involved.
This is a derivation of the equation for time dilation based on the classic light clock.
These are problems only involving the Lorentz factor and time dilation.
This is a derivation of the equation for length contraction based on calculating the length of an object involving relative motion.
These are problems only involving length contraction.
These are problems combining length contraction and time dilation. Relativity Problems II problems should make sense before you try these.
This is a derivation of the equation for relativistic momentum. I would ignore this, but it is needed to derive the mass energy equivalence in the next handout.
This is a derivation of E=mc2. Personally, getting to this point is one of my real goals in this unit since the equation is so famous, I figured it would be nice to see where it comes from.
Brief discussion of the energy equations derived, fission vs fusion, and units for energy
Describes the Correspondance Principle, and shows how the momentum and kinetic energy equations revert to their classic forms at low speeds. (This is trivial for momentum, but needs a series expansion to show it for kinetic energy.)
These are problems dealing with energy and momentum.
Shows how massless particles have the speed of light.
Here are the practice tests.
I made these only in the last couple years, and never really had the kids do these. I just like this stuff, and have dreams of adding more to this.
This is an introduction to spacetime diagrams. This handout is mostly qualitative and does not get into the correct scaling for multiple reference frames.
Questions making and interpreting spacetime diagrams. No scaled axes on this set.
This describes the invariant spacetime interval so that we can correctly scale the spacetime diagrams in the next handout.
This continues the description of spacetime diagrams and makes them more quantitative by using the spacetime interval to correctly scale multiple axes. There are a few questions at the end.
A nice application of spacetime diagrams to figure out relative velocities without Lorentz transformations.
This just asks two of the classic relativity paradoxes: the twin paradox and the barn-pole paradox.
This is the explanation. I used spacetime diagrams to help explain, so that is why they are placed here.
Explains geometric units, with some follow up problems. This is not needed for special relativity, but I think it is kind of cool, so I made the handout. I have never asked the kids to do this handout.
Derives the Lorentz transformations, which is a more formal way of doing special relativity. It also shows how you can get simultaneity, time dialtion and length contraction from there, as well velocity addition at high speeds. This is the more typical way to deal with an introduction to special relativity. I did write this one decades ago, but I never bothered to finish it (the first paragraph just sort of stops) or doo some follow-up with it.
Derives the wave equation. This probably doesn't make sense until you have had vector calculus, but it is needed to derive the speed of light. I just post this is an FYI for those who like advanced math.
Gives Maxwell's equations and calculates the speed of light from there. Need to know the wave equation first. Oh, and you need to know what curl and divergence are. This is only posted for those who really, _really_ like advanced math.
page last updated 6/21/23 by david mcclung, copyright 2023, all rights reserved.