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## Homework Statement

The balance wheel of a watch is a thin ring of radius 0.95 cm and oscillates with a frequency of 3.10 Hz. If a torque of 1.1x10

^{-5}Nm causes the wheel to rotate 45°, calculate the mass of the balance wheel.

## Homework Equations

I=mr

^{2}

T=(2π)sqrt(I/mgh)

τ=-Kθ

## The Attempt at a Solution

I got an answer but it's wrong...

Here's the work I did:

1.1e-5=-K(pi/2)

K=-7.003e-6

19.5 rad/s = sqrt (7.003e-6/(M(0.0095m)

^{2}))

380.25 rad/s

^{2}= 7.003e-6 Nm / 9.025e-5m M

M*0.0343 m/s

^{2}= 7.003e-6 Nm

m = 2.04e-4 kg

The answer should be 0.41g

(I realized just now that I took the square root of a negative number earlier. I tried to redo the problem but I'm still stuck...) Thanks!