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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

Respuesta :

Answer:

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

samueladesida43

The mass of the clay used by the potter at moment of inertia of 24 kgm² and is spinning freely at 40.0 rpm is 4.2kg.

How to calculate mass?

According to this question, the following information are given:

  • 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

Using the conservation of angular momentum

I₀ w₀ = I w

24× 40 = 24 + m × (1.20)² (32)

960 = 24 + m × 46.08

960 - 24 = 46.08m

936 = 46.08m

m = 4.2 kg

Therefore, the mass of the clay used by the potter at moment of inertia of 24 kgm² and is spinning freely at 40.0 rpm is 4.2kg.

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