Finding torsion constant of the wire?

[jazzymanstan]

Homework Statement

A torsional pendulum consists of a disk of mass 450 g and radius 3.5 cm, hanging from a wire. If the disk is rotated through an angle of 45o and released from rest and oscillates with a frequency of 2.5 Hz, what is the torsion constant of the wire?

• A :
  
  1.7 x 10-3 N-m/rad
• B :
  
  0.068 N-m/rad
• C :
  
  34 N-m/rad
• D :
  
  5.4 N-m/rad
• E :
  
  0.86 N-m/rad

Homework Equations

Torque = -k(torsion constant) * theta
Torque = r * F*sin theta

The Attempt at a Solution

So i had to google "torsion constant equation" because i couldn't find an equation in my book so I am hoping this is the right equation. Then i used the second torque equation to find torque. I did T = .035m * (.45kg * 9.8(gravity))*sin(45) = .10914.

Then i plugged the answer for T into the first equation T = -k *theta. So .10914 = -k * (pi/4), i converted 45 degrees to pi/4 radians. Then I divided .10914/(pi/4) = .13896.

So my overall answer was .13896. This is not one the options above so i know I did not do something correctly. I'm almost positive its from not having the right equations for the questions.

Advice would be great, thanks everyone!

 

[jazzymanstan]

i solved it myself but i will leave it here for other people if they need help. ignoring all my work above, it is best to use equation

. Then you use the appropriate inertia equation, which in this problem you'll use I = .5*m*r^2. And then for T, use T = 1/f. Plug those equations into the original equation, and then plug the numbers in for the correct variables, and you should get the right answer. (mine was .068 N-m/rad)