A clock balance wheel has a period of oscillation of 0.250 s. The wheel is constructed so that its mass of 10.0 g is concentrated around a rim of radius 0.600 cm.
a) What is the wheels moment of inertia? kg m^2
b) What is the torsion constant of the attached spring? N m / rad
The Attempt at a Solution
starting with part a)
I have gone mr^2 and gotten 3.6x10^-7 so i assumed that answer didnt make sense, I thought it could be because it says the mass is concentrated around the rim so do i treat that as if it was a ring?
If so I know that dI = dm r^2
so ∫dI = r^2 ⋅ ∫dm
so I = r^2 M
where M is the mass of the whole ring system.
Am I correct in this working or was my first calculation correct ?