🌀 Moment of Inertia — two masses on a spinning rod

Rotational inertia depends on WHERE the mass sits, not just how much. General law: I = Σmᵢrᵢ² = m₁r² + m₂r². The two masses need NOT be equal — bigger spheres = more mass. Push them out (bigger r) and I grows as r²; the same torque then gives less angular acceleration (α = τ/I) so the spin ω builds up more slowly. Spheres are same-density, so radius ∝ ∛mass (10× mass ≈ 2.15× radius).
I = m₁r² + m₂r² = 9.00 kg·m²
α = (τ−b·ω)/I = 0.44 rad/s²
ω = 0.0 rad/s → settles at τ/b = 5.0
τ = 4.0 N·m   b = 0.8 (axle friction)