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

  • #1

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!
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,394
1,045

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.
 
  • #3
Yep, that's the question word for word.
 
  • #4
TSny
Homework Helper
Gold Member
13,267
3,547
What is 45o in radians?
 
  • #6
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.
 

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

Replies
6
Views
2K
Replies
2
Views
2K
Replies
10
Views
477
  • Last Post
Replies
2
Views
1K
Replies
1
Views
334
Replies
7
Views
8K
Replies
5
Views
1K
Replies
5
Views
1K
Replies
2
Views
981
Top