# Angular acceleration problem Help!

1. Sep 6, 2008

### akan

A space station is constructed in the shape of a wheel 23 m in diameter, with essentially all of its 7.9×10^5 kg mass at the rim. Once the station is completed, it is set rotating at a rate that requires an object at the rim to have radial acceleration g, thereby simulating Earth's surface gravity. This is accomplished using two small rockets, each with 150 N thrust, that are mounted on the rim of the station.

How long will it take to reach the desired spin rate?

Formulas:
T = rFsinTHETA
T = I {alpha}
I = MR^2

Finding anuglar acceleration:
2RF = MR^2 {alpha}
2F = MR {alpha}
2F/MR = {alpha}

Finding the desired spin rate:
a = v^2/r
= w^2r^2 / r
= w^2r
w = sqrt(a/r)
= sqrt(g/r)

Finding the time:
t = w/ {alpha}
= sqrt(g/r) * MR / 2F
= sqrt(9.81 / 23) * (7.9*10^5) * (23) / (2 * 150)
= 3.96 * 10^4

Mastering Physics says I am wrong. Where is the mistake?

2. Sep 7, 2008

### akan

Hello,

I don't believe that this is such a difficult problem that noone can help me with a proper solution... This is just basic Physics B. So please help me.

Thanks,
Anthony

3. Sep 7, 2008

### Staff: Mentor

23 m is the diameter, not the radius.

4. Sep 7, 2008

### akan

Wow, that's it? Wow... damn it. I read the problem many times over and never saw this stupid mistake. Thanks a lot. :)