# Sol HW9Q9 says I(initial)*omega(initial)=I(final)*omega(final) What concept is this? conservation of what?

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A playground merry-go-round of radius R = 1.80 m has a moment of inertia I = 275 kg · m2 and is rotating at 12.0 rev/min about a frictionless vertical axle. Facing the axle, a 27.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round?

asked Oct 20, 2013

## 1 Answer

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This question is about the conservation of angular momentum, which is defined as $$\vec L=\vec r \times \vec P=I\vec \omega.$$
This question is similar to the inelastic collision in linear case, in which the momentum before and after are the same and after the collision, the two objects have the same velocity. In this rotational motion case, the angular momentum $\vec L$ is conserved (be the same before and after collision). Also after hopping on the child and the merry-go-round will rotate together with the same angular velocity, which makes it easier to calculate the angular momentum after the "collision". Note that here you will need to use $I$ instead of mass in the linear motion situations.
answered Oct 20, 2013 by (21,750 points)