Question

NASA Nick is building a wheel-shaped space station. He wants it to rotate about its center with a
period equal to the Earth’s rotation (24hrs) and he wants it to simulate the Earth’s gravity (1g).
What radius and speed would the space station need to have?

Answer 1

you can easily find this by knowing the mass of the earth and the distance of satellite from the center of the earth.

Answer 2

1. The centripetal force of spinning wheel space station will follow the equation for the tension in a string twirled with a weight on: F = mv^2/r

2. Divide both sides by the mass and you have g = v^2/r

3. An element of the outer arc is travelling at v= 2 pi r/T

4. Substitute into #2 with g=1 G, T=24 h. Solve for r. Substitute into #3 to find v.

Don't forget to convert T to mks units.