Glom

2004-Nov-30, 02:27 PM

A bunch of us started a civil war over how to do a problem about a rotating space station and apparent weight. The space station is a rotating cylinder of radius 25m generating 0.7G and an astronaut runs around the circumference at 5m/s both with and against the rotation in two different scenarios. The question asked us to calculate the astronaut's apparent weight in each case.

I did it by looking from the inertial frame at her speed around the circle. And then calculating the centripetal force. Easy. Others did it by looking at it from the rotating frame and adding the centrifugal inertial force and the coriolis force caused by her running. We got different answers and I figured out why.

By their method, a = ws²r + 2wsva, where ws is the angular speed of the station and va is the speed the astronaut runs in the station.

By our method, we said that

a = (vs + va)²/r

multiplying out, we get

a = (vs² + 2vsva + va²)/r

= vs²/r + 2vsva/r + va²/r

= ws²r + 2wsva + va²/r

So we have their centrifugal term and their coriolis term but there is also another term, which accounts for the difference. They deny that term is relevant to the problem and makes our answer wrong.

Who is right?

I did it by looking from the inertial frame at her speed around the circle. And then calculating the centripetal force. Easy. Others did it by looking at it from the rotating frame and adding the centrifugal inertial force and the coriolis force caused by her running. We got different answers and I figured out why.

By their method, a = ws²r + 2wsva, where ws is the angular speed of the station and va is the speed the astronaut runs in the station.

By our method, we said that

a = (vs + va)²/r

multiplying out, we get

a = (vs² + 2vsva + va²)/r

= vs²/r + 2vsva/r + va²/r

= ws²r + 2wsva + va²/r

So we have their centrifugal term and their coriolis term but there is also another term, which accounts for the difference. They deny that term is relevant to the problem and makes our answer wrong.

Who is right?