A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the student-stool system is 4.5 kg⋅m2. A second student tosses a 2.0 kg mass with a speed of 3.0 m/s to the student on the stool, who catches it at a distance of 0.45 m from the axis of rotation. What is the resulting angular speed of thestudent and the stool?

Question

Physics

Amani Jefferson

6 February, 20:09

A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the student-stool system is 4.5 kg⋅m2. A second student tosses a 2.0 kg mass with a speed of 3.0 m/s to the student on the stool, who catches it at a distance of 0.45 m from the axis of rotation. What is the resulting angular speed of thestudent and the stool?

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Answers (1)

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Anya · Answer 1

w = 0.55 rad / s

Explanation:

For this exercise let's use the conservation of angular momentum, let's write the moment in two moments

Initial

L₀ = r p + 0

L₀ = r mv

The first term is the angular momentum of the mass

Final

Lf = (I + m r²) w

Where I is the moment of inertia of the stool and the other term is the moment of inertia of the mass

L₀ = Lf

r mv = (I + m r²) w

w = m r v / (I + m r²)

Let's calculate

w = 2.0 0.45 3.0 / (4.5 + 2.0 0.45²)

w = 2.7 / 4.9

w = 0.55 rad / s