Experiments you can run yourself.
The moment of inertia I depends on how the mass is distributed (hoop mR², cylinder ½mR², sphere ⅖mR²). Racing down a ramp, the sphere wins — the least energy goes into rotation.
With no external torque the angular momentum L=Iω stays constant. Reducing the moment of inertia (pulling the mass in) increases the spin rate ω.
Torque M=F·r. A lever is in equilibrium when the sum of torques turning it left equals the sum turning it right (F₁r₁=F₂r₂). A longer moment arm lets you use a smaller force.
A rolling body carries two energies at once — which is why a ball rolls differently from a hoop.
A fast-spinning body keeps its axis direction. Angular momentum in action.