Rotational Motion

Honors students must read this. It might help AP students as well.

When things travel in a circle using our normal linear description of motion is very difficult. The direction of travel changes continually. For example, when you travel on a merry ground you may start out going west but then your velocity changes from west bound to south bound, then to east bound and then north bound, etc. So even with this simple motion your velocity is changing in a complex way, and so is your position.

However, it would be very simple to describe your motion using two numbers. One is your distance from the center of the merry ground, i.e. the radius of the circle your motion describes, and the second could be the angle theta, that your radius makes with the east . Then we could describe your position easily, saying for example, you are 7 meters from the center at an angle of 1.5 radians from east. We could describe your rate of motion as the rate of change of this angle. This would be called omega, your angular speed (radians/s) . If you measure the angle in radians, the distance you travel as you go around the circle is just radius x change in angle, i.e. distance = r delta Theta. Then your (tangential) speed (the old fashioned m/s) is just r x omega.

Try this for Monday:

Your are 3 m from the center of a carousel. The carousel turns half a turn, i.e. pi radians. How far did you move?

The carousel makes one complete rotation in 10 seconds, how far did you move in those ten seconds?

How fast were you going in m/s? This is your tangential velocity.

How many radians did it turn in those ten seconds? [ answer is 2 pi] How many radians did it turn in one second?

What was your angular speed (its called omega) in radians / second?

Was your tangential speed (m/s) equal to omega times 3 m?