Equivalent Moment of Inertia

Hi Guys, I'm having trouble finding the equivalent moment of inertia for a system. Basically it's a mass attached to a string, which is attached to a shaft. As the mass drops, the string unravels imparting some rotation on the shaft, this shaft rotates a small flywheel, and also rotates a second shaft via a geared system. This second shaft is attached to a second larger flywheel.

I've run some experiments and determined the frictional torque of the system. However, I can't work out how to find the equivalent moment of inertia. So far I have the energy balance equation:

(0.5I1w1^2 + 0.5I2w2^2 + 0.5mv^2) - T = 0.5 Ie w1^2

where w = angular velocity
T = frictional torque
I1, I2, and Ie are the two moments of inertia of the flywheel and the equivalent moment
v is the velocity of the weight as it falls
m is the mass of the weight

I have the radii of the flywheels, but not the masses, and I can replace w2 with an expression for w1 using gear reduction. Any tips on how I can perhaps eliminate some variables? I can't seem to find a way of solving this, without having the masses of the flywheels.

Where do you want to measure it at? The equivalent rotational inertia will be different on each shaft.

It looks a bit unsolvable without knowing the masses. Unless you know the acceleration.

To include the rotational inertia of the mass on the string, treat it as a point mass located at the radius of the drum. I = m * r2

Ah sorry, I want to find it for the shaft that the string is wound around. I can eliminate omega since it's a common term through gear ratios etc. It's just those moments of Inertia for each flywheel that's killing me.

Ah sorry, I want to find it for the shaft that the string is wound around. I can eliminate omega since it's a common term through gear ratios etc. It's just those moments of Inertia for each flywheel that's killing me.

What are the known variables? I still don't see why it isn't unsolvable.

I've worked it out, Thanks for your help. Turns out we needed to estimate the mass from density and it's dimensions. Made it a lot easier haha.