Calculating Rotations for a Space Station

[dani123]

Homework Statement

One design for orbiting space stations has a structure that is very much like a large bicycle wheel. The astronauts live on the inside of this wheel where the spinning provides an acceleration similar to Earth's gravity. Suppose the space station has a diameter of 125m .

a) What period of rotation would be required for the astronauts to experience an acceleration similar to the acceleration of gravity on Earth?

b) How many rotations would this space station have to make in one day?

Homework Equations

a_c=v²/r

v=2∏r/T

The Attempt at a Solution

A) we know that d=125m so r=62.5m and a=9.8m/s² T=?

So I started by finding V with a_c=v²/r equation and found that v=24.7487m/s

I then plugged that number into T=2∏R/v=15.87s per revolution.

B) For this part of the question I first had to break down how many seconds were in a day and found 1 day=86400seconds

Then I did, Δt/T=86400s/15.87s=5444 rotations in a day

So I would like for someone to look over my work and verify that I did it correctly and that my answers are good, and also if you could check that my significant figures are being respected! This would be very appreciated, thank you so much for your help and time! :)

 

[gneill]

Your method is fine and the numbers are good. As for significant figures, the only given value in the problem (the diameter at 125m) has three significant figures. That implies that you should display answers with the same number of significant figures (but retain more figures for intermediate results when you carry them forward into more calculations!)

Note that if you want to retain the level of precision then any values you introduce should have the same or greater precision. The acceleration due to gravity that you introduced has only 2 figures. Of course the problem statement says that you're looking for "an acceleration similar to Earth's gravity", which by strict interpretation might be anything of the same order of magnitude! Bit of a judgement call there. I think simply rounding your current answers to three figures will be acceptable.