Derivation of torsion equations

[ckeep]

Homework Statement

This is for a lab involving a torsional pendulum. We are given the equation below to use, but having not covered torsion, the lab manual says that "The student should look up the derivation of this formula."

Homework Equations

The equation we're asked to find the derivation for is:

C=(32LQ)/(\pid^4)

where C is the torsion modulus of the rod, Q is the torsion constant of the rod, L is the length of the rod, and d is the diameter of the rod.

The Attempt at a Solution

I have already derived the formula Q=[(2\pi)^2]*[I/(T^2)]

where Q is the torsion constant of the pendulum's rod, I is the moment of inertia of the object on the pendulum, and T is its period, but I've been entirely unable to find anything further in my book or on the internet.

 

[fresh_42]

A professional explanation of torsional pendulum



and an example for a lab report

https://faraday.physics.utoronto.ca/IYearLab/Torsion Pendulum.pdf