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A disk-shaped merryr-go-round has a radius of 1.5 m and a mass of 80 kg. A child of mass 25 kg stands 1 m from the axis of the disk while the system rotates with a = 1.5 s^-1 If the child walks toward the axis, what will the angular velocity of the systems be when she is 0.5 m from the axis?

Respuesta :

MathPhys

Answer:

1.8 rad/s

Explanation:

Angular momentum is conserved:

I₁ ω₁ = I₂ ω₂

For a solid disk, I = ½ MR².

For a point mass, I = mr².

So the total moment of inertia is:

I = ½ MR² + mr²

The initial moment of inertia is:

I₁ = ½ MR² + mr₁²

I₁ = ½ (80 kg) (1.5 m)² + (25 kg) (1 m)²

I₁ = 115 kg m²

The final moment of inertia is:

I₂ = ½ MR² + mr₂²

I₂ = ½ (80 kg) (1.5 m)² + (25 kg) (0.5 m)²

I₂ = 96.25 kg m²

Therefore:

I₁ ω₁ = I₂ ω₂

(115 kg m²) (1.5 rad/s) = (96.25 kg m²) ω₂

ω₂ = 1.8 rad/s

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