Calculating moment of inertia and torsion constant

[Erenjaeger]

Homework Statement

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

Homework Equations

I=mr^2[/B]

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 ?
[/B]

 

[haruspex]

3.6x10^-7

Assuming that's in kg m², that is correct. What bothers you about it?

 

[Erenjaeger]

Assuming that's in kg m², that is correct. What bothers you about it?

yeah I put the values into kg and m when I calculated, I just thought that because it was such a low number it was wrong.
say for example sake it was a ring, would my calculations I put down be correct to determine the moment of inertia??

 

[haruspex]

yeah I put the values into kg and m when I calculated, I just thought that because it was such a low number it was wrong.
say for example sake it was a ring, would my calculations I put down be correct to determine the moment of inertia??

mr² works for a point particle, a ring (about an axis through the centre of the ring and normal to its plane) and a hollow cylinder (about the axis of the cylinder). In each case, each part of the object is at the same distance from the axis.

 

[David Lewis]

The radius at which all the mass is assumed to be concentrated (for calculation purposes) is also called the radius of gyration.