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Frat House Physics Tutor

After getting my BA (Math and Physics double major) I went to grad school in Physics at U. Illinois Urbana. If I had the choice over again, I'd have gone almost anyplace else.

My source of income was a half-time teaching assistant, in Freshman Physics Recitation and Lab, mostly teaching Engineering Students. There happened to be a room available at the local chapter of my fraternity. In that case, too, if I had to choose over again, I'd have lived almost anywhere else. The students' minds were far from being on academics.

But the Local Fraternity Alumni heard about my request to live at the Frat, and my status as a grad student. Would I consider a free room, if I'd spend say an hour a day as Chapter Academic Advisor? Sure.

Almost nobody was interested in even setting quiet hours for study time. There were, however, two students taking introductory Physics. They both came to me asking for help on planning a project for their class, that counted for much of the grade. So I suggested two historical experiments, with simple requirements to make it work today, and let them choose.

One project was measuring the speed of light by using a spinning disk with many slits cut radially along the edge. For example, the disk could be a 10 inch circular saw blade, made for cutting sheet metal; such blades were commercially available and reasonable. Suppose it has 10 slots per linear inch around the edge of the blade, or about N = 10* 2 * pi * R slots, where R = the radius of the blade, about 5 inches. or about N = 315. Further suppose that the slots are narrow, about 1/100 inch.

Shine a bright, collimated, light through a fixed "sending" slot of the same size and orientation as exactly one slot in the disk. Point the light coming out of the slot toward a distant high-quality reflector (a 3 foot square covered with white reflective tape, or a piece of plywood with many white bicycle reflectors) a measured mile distant. When the disk is stopped, this light is continuous; when the disk is rotated, there are n pulses per second, where n = (N slots around the disk) * (r revolutions per second).

Look through a different, but synchronized "receiving" slot, say on the opposite side of the disk, at the distant reflector, with a small telescope. Vary the speed of the disk smoothly by some method, such as a variable voltage ac/dc motor, and accurately time the rotation rate.

In practice r is about 3600 RPM = 60 revolutions/sec maximum, so n = 18,900 pulses per second. At this rotation rate and slot size, the pulse width is about 1/10 the pulse cycle time, or 1/(10 * 18,900) of a second, or 1/200000 sec. These pulses are about 1 mile long in space, or half of the distance between sending slot and receiving slot.

What you see is this: When the disk is still, a bright continuous light. As you start the disk rotating and speed it up enough, the pulses get shorter because the "sending" slot is only lined up with a slot in the disk for part of the time. Part of the light pulse being sent doesn't reach the receiving slot before the receiving slot turns past the point where the receiving telescope is focused. So as the speed increases, the view slowly darkens, until it goes completely dark. As the disk continues to spin faster [this may require making a bigger disk, say a meter in radius, with slots every millimeter] the light will again be visible, because the inter-pulse time is so short that there are now TWO pulses in flight by the time the receiving slot is open.

Then c = (total distance traveled by the pulse seen = 2 miles) / (time between two successive openings of receiving slot) or approximately c = (2 miles) / (1/(2* 10* 18,900 )sec) = 189,000 miles/sec which is close to the textbook value approximating 186,000 miles/sec.

Both students got A's on their term papers.