The physics
The moment of inertia I shows how hard a body is to spin up. It depends on the mass. It also depends on how far the mass sits from the axle.
point masses: I = Σ m r²
Each standard shape has its own rule. Check the axle each rule is for.
ring: MR² disc: ½MR² solid ball: (2/5)MR² hollow ball: (2/3)MR²
Take a ring with the same mass and the same I. Its radius is the radius of gyration k.
I = M k² k = √(I / M)
The test rig: a 0.5 kg weight hangs from a cord round a 10 cm drum. It drops 1 m and spins the body up. A bigger I spins up slower, so the drop takes longer.
a = m g / (m + I / r²) t = √(2h / a)
A body that spins and moves at once has two kinds of kinetic energy. Add them.
KE = ½ Icm ω² + ½ M v²