# Torque and precession

## Main Question or Discussion Point

Question
The Hubble Space Telescope is stabilized to within an angle of about 2 millionths of a degree by means of a series of gyroscopes that spin at 1.92×104 rpm . Although the structure of these gyroscopes is actually quite complex, we can model each of the gyroscopes as a thin-walled cylinder of mass 2.00 kg and diameter 5.00 cm , spinning about its central axis.

How large a torque would it take to cause these gyroscopes to precess through an angle of 1.20×10-6 degree during a 5.00 hour exposure of a galaxy?

Equations
I=mr2
L=Iω
Ω=dΦ/dt
τ=ΩL

Variables and Conversions
m=2.00kg
r=0.025m
dt=5×60×60=1800s

Attempt at Solution

I=(2.00kg)(0.025)2=1.25×10-3kgm2
L=(1.25×10-3kgm2)(640π)=4π/5
Ω=(2.09×10-8)/(1800)=1.16×10-12

τ=(1.16×10-12)(4π/5)

=2.92×10-12Nm

My answer is incorrect. Any help would be greatly appreciated. This is the ridiculous "mastering physics" website. It is the most pointless thing ever. I would much rather we were given an assignment to complete as at least then you can receive constructive feedback as opposed to simply being told the answer is wrong.

I am happy to be wrong as long as I can understand why. I am sure I have just made a simple mistake, like use the wrong equation or miscalculate something, but with no guidance I can't fix it.

Thank you.

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Homework Helper
Gold Member
It looks almost completely correct to me, but I found one arithmetic mistake: $\Omega =1.16 E-11$. (You missed the exponent by one unit). At least I think that's one place that needs a correction.... editing..that would make the answer 2.92 E-11 if everything else is correct, which I think it may be.

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Well, I'm not sure if you can call it helpful, but I don't see anything wrong with this. I am 99.9% sure this is the right approach, and I checked almost all of the math. (I could only approximate multiplying by pi in the last step. doing it in my head while lying in bed.)

It looks almost completely correct to me, but I found one arithmetic mistake: $\Omega =1.16 E-11$. (You missed the exponent by one unit). At least I think that's one place that needs a correction.... editing..that would make the answer 2.92 E-11 if everything else is correct, which I think it may be.
I suck. What hurts more than having said I didn't see anything wrong is saying so AFTER you already found this mistake. Jeez.

Homework Helper
Gold Member
I suck. What hurts more than having said I didn't see anything wrong is saying so AFTER you already found this mistake. Jeez.
That tends to re-enforce my belief that this might be the OP's only error. Looking forward to hearing from the OP.

Thank you all for the replies, turns out there was a mistake in the system and my answer of 2.92*1012 was correct after all. Had this verified by 3 lecturers at uni today.

You can all sleep easy now.

Thanks again.

Very good, except when you said you had the correct answer after all, I was pretty sure there must be a second error and I found it: $dt=(5)(60)(60)=18000$, instead of 1800. Glad you got the right answer, but looks like you had offsetting errors.