Rock and string question

1. May 3, 2015

Curly

A couple of simple, (maybe dumb) questions -

Consider a string, maybe a meter long, with one end attached to a small rock, and the other end attached to the shaft of a motor standing so the shaft points upwards. When the motor is turned off, the string hangs limp. When the motor runs, the rock and string swing around in a circle like the blades of a helicopter, due to the tension in the string constantly forcing the velocity of the rock to change direction in a circular orbit. What produces the tension in the string? If it is the momentum of the rock, then the rock must have velocity. If the rock has no velocity, it has no momentum. This is where it gets confusing -

Imagine that the motor is mounted inside a windowless room that sits atop a giant turntable similar to a merry-go-round, so that the entire room can be made to spin. If the motor is turned off, but the turntable supporting the room is made to rotate at the same velocity as the motor does when it runs, then there will be the same tension in the string, and the rock will swing around in the same manner as it did when being spun by the motor, but now the string and rock are motionless relative to everything inside the room, since the entire room is spinning along with the string and rock on the same axis. If nothing is moving inside the room containing the rock, the rock has no velocity relative to the room or anything inside it. However, the rock must have velocity relative to something to create the momentum that causes the tension in the string. What then is the velocity of the rock relative to?

In this particular case, the angular velocity of the turntable supporting the room could be measured relative to the earth upon which it sits, and a reasonably accurate tension in the string could be calculated, but what about in the general case? For example the space wheel in the movie 2001, that spins to simulate gravity? What is its spin relative to? The difficulty with using an external object or entity as a reference point to measure angular velocity, seems to me to be. that an external object may itself have angular velocity about the same axis of rotation, as is the case in the above example. What reliable means of establishing the angular velocity of something is available, other than by measurement of the force that the angular velocity creates? What connection is there between the rock and string inside the sealed room and what is happening outside the room? How do the rock and string inside the windowless room "know" that they are spinning?

2. May 3, 2015

Staff: Mentor

They know because that is the way a rotating frame of reference works. They don't have to measure their rotation against anything.

3. May 3, 2015

A.T.

If you don't want to measure forces on objects that are static in a frame, you can also throw stuff around and analyze it's trajectories in that frame, in order to determine that the frame is rotating. From the Coriolis and centrifugal accelerations you can deduce the angular velocity of the frame: