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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Homework Help: Angular acceleration problem Help!

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