# Calculating moment of inertia and torsion constant

#### Erenjaeger

1. The problem statement, all variables and given/known data
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

2. Relevant equations
I=mr^2

3. 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 ?

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#### haruspex

Homework Helper
Gold Member
2018 Award
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

Homework Helper
Gold Member
2018 Award
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.

"Calculating moment of inertia and torsion constant"

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