A potter's wheel, with rotational inertia 49 kg·m2, is spinning freely at 40 rpm. The potter drops a 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?

Question

Physics

Pierce Maxwell

16 August, 08:39

A potter's wheel, with rotational inertia 49 kg·m2, is spinning freely at 40 rpm. The potter drops a 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?

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Answers (1)

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Jordyn Holt · Answer 1

8.5 kg

Explanation:

Angular momentum is conserved.

I₁ ω₁ = I₂ ω₂

I ω₀ = (I + mr²) ω

(49 kg m²) (40 rpm) = (49 kg m² + m (1.2 m) ²) (32 rpm)

61.25 kg m² = 49 kg m² + (1.44 m²) m

m = 8.5 kg

The mass of the clay is 8.5 kg.