Angular Momentum: A light-weight potter's wheel, having a moment of inertia of 24 kg ∙ m2, is spinning freely at 40.0 rpm. The potter drops a small but dense lump of clay onto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm, what is the mass of the clay? A) 4.2 kg

4.2 kg

Explanation:

I' = moment of inertia of potter's wheel = 24 kgm²

w₀ = initial angular speed of the system = 40.0 rpm

w = final angular speed of the system = 32 rpm

m = mass of the clay = ?

r = distance of clay from axis of rotation = 1.20 m

I₀ = Initial moment of inertia of the system = I' = 24 kgm²

I = final moment of inertia = I₀ + m r² = 24 + m (1.20) ²

Using conservation of angular momentum

I₀ w₀ = I w

(24) (40) = (24 + m (1.20) ²) (32)

m = 4.2 kg