Extra Credit: Spinning the Great Pyramid

This project must be done by individuals.

High Priest Ptene walks up to Chief Architect Amose as he stands next to the just-completed Great Pyramid of Giza. Ptene says, "I have some good news and some bad news. Which do you want to hear first?"

Amose says, "Give me the good news."

"Well, the pyramid meets all the specs: it is exactly H = 146 meters tall, with four sides each L = 230 meters in length. The mass M = 6 billion kg is right in the middle of the desired range. And that frictionless bearing you put under the center is very nice."

"Great!" says Amose, "So what's the bad news?"

"The bad news is that it is facing the wrong direction: the side with the big E painted on it is supposed to face East, not West. As it stands now, it will curse the Pharaoh when he dies, not help him to reach the Land of Bread and Beer. You need to rotate the entire structure 180 degrees."

"Aarrrrrgggghhhhh!" cries Amose.

"Oh," adds Ptene, "all the workers have gone home, so you'll have to do it yourself. You'd better hurry -- the big Grand Opening Ceremony is tomorrow at noon, and the Pharaoh doesn't like to be kept waiting."

Ptene leaves. Amose curses for a moment, then steadies himself. "It's okay," he thinks, "all I have to do is apply a constant force by pushing at one of the corners. First, I'll increase the angular velocity from zero to something ... then, when the pyramid has rotated 90 degrees, I'll turn around and push the OTHER way, so that I gradually slow the pyramid down. When it has rotated another 90 degrees, it will come to rest. Brilliant!"

Amose starts pushing, with a constant force of F = 500 Newtons. If he follows his plan, how long will it take him to rotate the pyramid by the required 180 degrees?

You must show all your work in order to receive credit for this project.

This page maintained by Michael Richmond. Last modified Nov 30, 2007.