Problem: A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round with a mass of 240kg is spinning at 20rpm. John runs tangent to the merry-go-round at 4.0m/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?

FREE Expert Solution

We'll solve this problem using conservation of angular momentum:

Moment of inertia of a disk about its center:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{M}}{{\mathbf{R}}}^{{\mathbf{2}}}}$

Moment of inertia of a point mass:

$\overline{){\mathbf{I}}{\mathbf{=}}{\mathbf{M}}{{\mathbf{R}}}^{{\mathbf{2}}}}$

Angular velocity:

$\overline{){\mathbf{\omega }}{\mathbf{=}}\frac{\mathbf{v}}{\mathbf{R}}}$

John can be modeled as a point mass.

Initial angular velocity of the merry-go-round:

R = d/2 = 3.0m/2 = 1.5 m

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Problem Details

A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round with a mass of 240kg is spinning at 20rpm. John runs tangent to the merry-go-round at 4.0m/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?