# 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:

ωi = 20 rev/min (1min/60s)(2π rad/rev) = 2π/3 rad/s

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

95% (68 ratings) ###### 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?

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Our tutors have indicated that to solve this problem you will need to apply the Angular Collisions with Linear Motion concept. You can view video lessons to learn Angular Collisions with Linear Motion. Or if you need more Angular Collisions with Linear Motion practice, you can also practice Angular Collisions with Linear Motion practice problems.