Conservation of Angular Momentum Video Lessons

Concept

# Problem: A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 125 kg•m2. When one person is standing at a distance of 1.50 m from the center, the carousel has an angular velocity of 0.700 rad/s. However, as this person moves inward to a point located 0.750 m from the center, the angular velocity increases to 0.870 rad/s. What is the person's mass?_____ kg

###### FREE Expert Solution

We 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 carousel and m2 to be the mass of the person.

Using the parallel axis theorem, the moment of inertia is given by:

$\overline{){\mathbf{I}}{\mathbf{=}}{{\mathbf{I}}}_{{\mathbf{c}}}{\mathbf{+}}{\mathbf{m}}{{\mathbf{r}}}^{{\mathbf{2}}}}$

Now, the initial moment of inertia:

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###### Problem Details

A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 125 kg•m2. When one person is standing at a distance of 1.50 m from the center, the carousel has an angular velocity of 0.700 rad/s. However, as this person moves inward to a point located 0.750 m from the center, the angular velocity increases to 0.870 rad/s. What is the person's mass?
_____ kg