Calculating the mass of the wheel on a pendulum on a watch

AI Thread Summary
The discussion focuses on calculating the mass of a watch's balance wheel, given its dimensions, frequency, and applied torque. The user initially calculated the mass as 2.04e-4 kg but noted that the correct answer should be 0.41g. They identified an error in their calculations, specifically taking the square root of a negative number. The conversation highlights the importance of careful mathematical operations and unit conversions, particularly converting degrees to radians. The user expresses frustration over common mistakes but appreciates the assistance in clarifying their errors.
NathanLeduc1
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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=mr2
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/s2 = 7.003e-6 Nm / 9.025e-5m M
M*0.0343 m/s2 = 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!
 
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NathanLeduc1 said:

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=mr2
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/s2 = 7.003e-6 Nm / 9.025e-5m M
M*0.0343 m/s2 = 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!
Is that the complete problem, word for word.

It seems that some information is missing. I could guess at what's missing, but it would be just a guess.
 
Yep, that's the question word for word.
 
What is 45o in radians?
 
pi/4
 
Oh my goodness... I just realized why you were asking me that. Wow, I am dumb. Man, those stupid mistakes get me every time. Thanks for the help.
 
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