Calculating the torsion constant

[andreaumali]

Homework Statement

A thin metal disk with mass 2.00E-3kg and radius 2.20cm is attached at its center to a long fiber. The disk, when twisted and released, oscillates with a period of 1.00s. Find the torsion constant of the fiber.

Homework Equations

a) ω=sqrt(κ/I)
b) f=1/(2π) sqrt(κ/I)
where ω=angular frequency, κ=torsion constant, I=inertia, f=frequency

The Attempt at a Solution

Is the inertia of this thin disk simply 1/2 MR^2?
Is the angular frequency 2π/1.00s?
and do I simply plug in these variables into eqtn (a) to solve for κ?

 

[haruspex]

Yes, yes and yes.