- #1
Melawrghk
- 145
- 0
Homework Statement
I have to show the formula derivation of this:
[tex]T=2*pi*\sqrt{\frac{2IL}{pi*r^{4}*G}}[/tex]
based on the fact that I know this:
[tex]\tau=I\alpha=\frac{pi*G*r^{4}}{2L}\theta[/tex]
Homework Equations
See above
The Attempt at a Solution
Well, I know T=2pi/[tex]\omega[/tex] and [tex]\alpha=\Delta\omega/\Delta(t)[/tex]
So I decided to just get an equation for omega from the expression for tau.
So I had:
d[tex]\omega[/tex]/dt=[tex]\frac{pi*G*r^{4}}{2IL}\theta[/tex]
Which looked promising until I integrated both sides wrt 't' and got:
[tex]\omega=\frac{pi*G*r^{4}}{2IL}\theta*t[/tex]
And this really gets me nowhere and I don't know what else to do. Thanks in advance for the help!