PH253: Exam note #1

A quantity like "35000 revolutions per minute" is an angular velocity. Say you have disc spinning at an angular velocity (omega), and you are interested in the linear velocity at a point a radial distance r=0.1m from the center of the disk. The velocity calculation goes like this:

v = r\omega = \left(0.1\,\text{m}\right)\left(35000\,\frac{\text{rev}}{\text{min}}\right)\left(\frac{1\,\text{min}}{60\,\text{sec}}\right)\left(2\pi\,\frac{\text{rad}}{\text{rev}}\right)\approx 370\,\frac{\text{m}}{\text{s}}

First, you need to convert the angular velocity to radians per second (or just 'per second' since radians are really just a ratio, and thus unit-less). Then you can multiply by the radial distance from the point of rotation to get the regular velocity or speed at that point on the disk.

That's my main comment on problem 1 of the exam. The second one being that the time dilation factor is just the ratio between the time elapsed at the rim of the disc to that at the center (which is at rest). The ratio is just (gamma) - we don't need to use the full Lorentz transformation, because there is no significant spatial separation, and we are talking about different parts of the same object.

PH253: Exam, last-minute things

Don't forget your calculator ... there are not many numbers on the test, but just enough.

Today

I'll be in Gallalee all day. From 2-5pm, I"ll be in room 322 running a lab, but feel free to come by for quick questions.

PH253: more practice problems

UPDATE 5: some typos fixed, particularly one in problem 10 just above equations 36-39. The sentence fixed was "The muon has both kinetic energy and rest energy, and we can write its total energy in terms of ..." The prior version said "... write its total kinetic energy ..." which is incorrect.

UPDATE 4:  all problems should have solutions now. I also realized that partial derivatives are beyond the stated math prereq, so you can ignore problem 11 ... something like that will not be on the exam.
UPDATE 3:  answers for all but 11 are included and some typos in the problems fixed.
UPDATE 2:  answers for all but questions 6, 8, 11 are there.
UPDATE: answers for about half the problems are up now. Should have the rest done in an hour or so.

Here you go. These are much closer to real exam problems. Read the general comments as well: one or two of these problems might just show up on the exam with little or no modification.

Answers & some solutions will follow later today.

UPDATE: I scratched the first problem (density and so forth) on further reflection.

PH253: Exam practice problems

Just to get you started, here are some questions from the text that are worth looking at:

Section 1:

• Example 1.7
• Exercises 3,4,5,6,12
• Problem 6

Section 2:

• Exercises 3, 11, 12
• Problem 3

These are relatively simple problems, but concerning topics that are very likely to show up on the exam. I'll be posting some more in-depth problems shortly for you to practice on. These will very closely resemble what the exam will look like.

Thanks ...

... to many of you for sending in sensibly-named files :-)

Example test problems coming tomorrow. For now, check out this, and this.

If you're not feeling mathy, try some animations. This page has some nice ones that let you see the difference between phase and group velocity nicely, as well as how the wave packet spreads (so you can see how the uncertainty in localizing the associated particle changes).

Research Opportunity

A colleague just asked me if I knew any undergrads interested in spending the summer doing an internship at Argonne national lab. The project would involve developing an electrostatic switch using ultrananocrystalline diamond films. If you don't know what that means, it would be working with a lot of really cool vacuum and electronic equipment. :-) Travel money and stipend are likely to be covered.

If you were thinking about a research internship for the summer, and have an interest in the solid state physics or ECE areas, it might be something worth looking in to. Let me know if you'd like to know more, I'll put you in contact with my colleague.