Recent content by rocketcity

turin, that's what I meant. He writes it \delta _\mu to indicate that the derivative w.r.t. the contravariant components is a covariant operator. I suppose 'derivative w.r.t. a vector' is my terminology, not his--all I meant was that it's a compact way of saying 'take four different...

I agree with the temperature change--actually, I got 0.597 degrees using 4.186 Joules = 1 calorie. For the speed, are you using wavelength*frequency = speed ? Notice that the wavelength is in centimeters; I got 0.2 m/s. Another question: do circular wavefronts on the water's surface...

My mechanics/EM professor uses the 'derivative with respect to a vector' notation quite a bit--in tensor calculus, it's actually acceptable (and powerful--since the tensor calculus we're using is just a Cartesian space with time tacked on.) I can sort of picture this array of derivatives, but...

In a vacuum, Maxwell's Equation (differential form) reduce to \nabla * E = 0 \nabla * B = 0 \nabla \times B = \epsilon_0 \mu_0 \frac{\delta E} {\delta t} \nabla \times E = -\frac{\delta B}{\delta t} These are obtainable from the integral forms Sitewinder mentioned...

To any of the crude (but clever) ways of estimating time lapse you suggested, I would affix a 'give or take a factor of 2'--meaning that if you estimate the car was moving 20 mph, I would say that the actual value was between 10 and 40mph--not very useful in determining whether the pedestrian...

If the pipe heats up, then it's increasing the surface area over which heat can dissipate into the cooler environment. Now that I think about it, though, that pipe is not that large compared to the surface area of the laptop that's already getting fairly hot. I still think you should...

You can get a new Halliday and Resnick for something like $140 bucks--or you can buy a 2000 edition for $0.75 on half.com. (Undergraduate texts are generally devalued to Sears and Roebuck catalog status as soon as the professors switch to a newer edition.) I've heard that saying...

1. Bring two identical pots of water to a boil. 2. Remove pots from heat, wait a few minutes. 3. Place one pot on the laptop cooler, place the other one on whatever table you normally rest the laptop on. 4. Put a thermometer in each pot; record temperature versus time for several...

I think Marion and Thornton is the way to go. I pity anyone who had to learn from the venerable Goldstein without Marion and Thornton to back him up. I also think M. Boas' introduction to the variational principle (upon which Lagrangian mechanics is based) is invaluable. The Euler-Lagrange...

Why do all of the 'popular' physics texts (i.e., non-textbooks meant to be read by the masses) eschew equations? I picked one up that had an interesting title, saw on the back that it had a cartoon of a chalkboard with a professor happily writing NO EQUATIONS, and promptly put it down. This...

The same question in different words: How fast would a satellite have to travel to stay in orbit just a few centimeters above the Earth's surface? It's all a matter of acceleration due to gravity matching centripetal acceleration--or, in my non-inertial frame, force of gravity matching...

Sunlight offers whatever it collides with on the Earth's surface with about 1000 Watts of radiant power per square meter. A 'good' black box will absorb most of that energy; a 'good' white paint (developed for that purpose) can scatter most of it away. Since most paints are designed not to...

What angle the two bodies will go flying off at after the collision is highly dependent on how they strike. Think about lining up a pool shot: the six ball is stationary, and the cue ball is traveling due north towards it at a certain speed. Depending on where on the six ball you hit it, the...

I find it interesting--and baffling--that the gravitational force and the electrostatic force can be so empirically similar and yet give rise to such completely different theory. Why do we not explain electrostatic attraction by saying that the presense of a *charge* warps space-time? Why do...

I like the angular momentum argument best, because it works even in the classical limit. The higher you make the tower, the slower the world turns. THEN take into account the relativistic effects on mass and kinetic energy. Finally, realize that the earth-tower system would rotate about...