Space Station and Arificial Gravity

[wolly6973]

A space station is shaped like a ring and rotates to simulate gravity. If the radius of the space station is 150 m, at what frequency must it rotate so that it simulates Earth's gravity? [Hint: The apparent weight of the astronauts must be the same as their weight on Earth.]

Once again I cannot find formulas to even start this! What should I be using for this problem?

 

[mrjeffy321]

Since both in space and on the Earth the astronauts' mass will be the same, in order to simulate gravity one would need to create some type force to act on the astronauts, causing them to accelerate at the same rate caused by gravity.

In the case of a spinning wheel, this acceleration is centripetal acceleration.
You need to set the centripetal acceleration of an object placed at a distance of 150 meters from the axis equal to the gravitational acceleration on the surface of Earth,
g = v^2 / r
Solving this will give you the speed of rotation, but you are looking for frequency. Find a relationship between the speed of rotation, the circumference of the wheel, and time in order to calculate frequency.

 

[wolly6973]

So that would be v=2pir/t. But what units is that answer in. I need rev/s

 

[mrjeffy321]

Revolutions per second would be your unit of frequency.

Since the object is traveling in a circle and you know its tangential speed at any point along that circle you might say that it has a certain angular velocity which it is rotating.
The angular velocity is given as the tangential velocity divided by the radius of rotation.
The units of angular velocity are radians per second...this is still not what you want though.
However, you know that for every 2*pi radians the object moves (one complete circle), this equals 1 complete revolution. Dividing the angular velocity by 2*pi should then give you units of rev. / s.

You’re looking for how many times the object can go around the complete circle in 1 second. How far does the object travel at its given speed in 1 second…then express this as a fraction of the total circumference.