# Moments of Inertia

1. Jan 18, 2010

### physicsfun_12

1. The problem statement, all variables and given/known data
I linear spring has one end attached to a ceiling, the other end hanging freely. It was noted that the spring was extended by 120mm when a mass of 2.5kg was attached at the bottom.

If the moment of inertia of the mass is 10kg.m2 about its vertical axis, calculate the maximum angular velocity of the spring when the system is released from from the 360 degree twisted position. Assume no change in height and the system is conservative.

I am not to sure how to approach this. I think it may have something to so with the following formulas:

2. Relevant equations
K.E=1/2.K.theta2 and K.E=1/2.I.w2

where k=torsional stiffness, I=moment of inertia and w=angular velocity

3. The attempt at a solution
Other than those equations, I'm really not sure.

Any help much appriciated with this, thanks in advance.

Mike

2. Jan 18, 2010

### Yitzach

Wikipedia informs me that $$\kappa$$ is also called the spring constant. The reason for the "2.5 kg mass extends the spring 120 mm" is so you can find it using Hooke's law where k is preferred. You should be able to get much closer to the answer with that.