A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter mer

Question

A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round with a mass of 290 kg is spinning at 24 rpm. John runs tangent to the merry-go-round at 6.0 m/s, in the same direction that it is turning, and jumps onto the outer edge. John's mass is 30 kg.
What is the merry-go-round's angular velocity, in rpm, after John jumps on? A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round with a mass of 290 kg is spinning at 24 rpm. John runs tangent to the merry-go-round at 6.0 m/s, in the same direction that it is turning, and jumps onto the outer edge. John's mass is 30 kg.
What is the merry-go-round's angular velocity, in rpm, after John jumps on?
What is the merry-go-round's angular velocity, in rpm, after John jumps on?

Explanation / Answer

Angular speed of merry-go-round before:
1 = 24 rev/min * (2 rad/rev) * (1min/60s) = 2.513 rad/s

This is a conservation of angular momentum problem.

I 1 + r (m_J v) = (I + m_J r²) 2
2 = (I 1 + r (m_J v)) / (I + m_J r²)

Moment of inertia of solid disc:
I = ½ M r²
I = ½ * 290 kg * (3.0 m / 2)²
I = 326.25 kgm²

2 = (I 1 + r (m_J v)) / (I + m_J r²)
2 = (326.25 kgm² *2.513 rad/s + (3.0 m / 2) * 30 kg * 6.0 m/s)) / (326.25kgm² + 30 kg * (3.0 m / 2)²)
2 = 2.793rad/s
2 = 2.793rad/s * (rev/2 rad) * (60s/min) = 26.67 rev/min = 26.67 rpm

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