Conservation of Angular Momentum Video Lessons

Concept

# Problem: A playground merry-go-round with a mass of 125 kg and a radius of 1.9 m is rotating with a frequency of 0.42 rev/s.What is the magnitude of its angular velocity, in radians per second, after 17 kg child gets onto it by grabbing its outer edge? The child is initially at rest.

###### FREE Expert Solution

In this problem, we'll use the conservation of angular momentum, given by:

$\overline{){{\mathbf{I}}}_{{\mathbf{0}}}{{\mathbf{\omega }}}_{{\mathbf{0}}}{\mathbf{=}}{{\mathbf{I}}}_{{\mathbf{f}}}{{\mathbf{\omega }}}_{{\mathbf{f}}}}$, where I0 and Iare the initial and final moments of inertia and ω0 and ω0 are the initial and final angular velocities.

Let's take m1 to be the mass of the merry-go-round and m2 to be the mass of the child.

The initial moment of inertia:

$\begin{array}{rcl}{\mathbf{I}}_{\mathbf{0}}& \mathbf{=}& \frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}_{\mathbf{1}}{\mathbf{r}}^{\mathbf{2}}\\ & \mathbf{=}& \mathbf{\left(}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\right)}\mathbf{\left(}\mathbf{125}\mathbf{\right)}\mathbf{\left(}\mathbf{1}\mathbf{.}{\mathbf{9}}^{\mathbf{2}}\mathbf{\right)}\end{array}$

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###### Problem Details

A playground merry-go-round with a mass of 125 kg and a radius of 1.9 m is rotating with a frequency of 0.42 rev/s.
What is the magnitude of its angular velocity, in radians per second, after 17 kg child gets onto it by grabbing its outer edge? The child is initially at rest.