# Moments of inertia in flywheel

I have managed to rearrange an equation give to me to make I (moment of inertia) the subject. I am now having problems working out the values for parts of it.

I = moment of inertia
m = mass
g = gravity
h = height
v = translational speed of the mass falling
Tf = work done against friction
theta = angle through which flywheel rotates in radians
w = rotational speed of the flywheel

The equation is I = (1/2mgh - mv^2 - Tf * theta) / w^2

I am finding it hard to work out a value for v and w. is 'the translational speed of mass falling (v)' is that just a fancy way of saying velocity?

I am unsure of how to find a value for w

Hope this makes sense

Thanks

v is the linear or translational speed in units of m/s

w is the angular speed in radians/s

Doc Al
Mentor
Can you describe the problem you are trying to solve?

After getting some results from experiments in the labs from the flywheel, measuring the time it takes for a mass to fall from a set height and the critical mass. I have to determine the moment of inertia I of the flywheel and its axle to estimate the frictional torque.

The problem i am having is trying to find values for v and w. is there equations for these?

Thanks

Doc Al
Mentor
If the mass is falling from rest and you have measured the height it fell and the time it took, you can calculate the average and final values of its speed v. And ω and v are related.

Doc Al
Mentor
The equation is I = (1/2mgh - mv^2 - Tf * theta) / w^2
You might want to double check that formula.

Ah yes didnt write it properly should be I = mgh - 1/2mv^2 - tf *theta / 1/2w^2

Thanks