A playground carousel is rotating about its center.The radius of the carousel is 1.50 m,its initial angular speed is 3.14 rad/s and its moment of inertia is 125 kg m².A 40.0-kg person climbs onto the carousel near its outer edge.What is the angular speed of the carousel after the person climbs aboard? A)1.41 rad/s B)1.57 rad/s C)1.83 rad/s D)3.14 rad/s

Question

Quizplus · Accepted Answer

Conservation of angular momentum can be used to solve this problem. Before the person climbs aboard, the initial angular momentum of the system is:
L1 = Iω1
where I is the moment of inertia, ω1 is the initial angular speed.
After the person climbs aboard, the moment of inertia of the system changes. The new angular momentum of the system is:
L2 = (I + mr^2)ω2
where m is the mass of the person, r is the radius of the carousel.
Conservation of angular momentum gives:
L1 = L2
Iω1 = (I + mr^2)ω2
Plugging in the given values, we have:
125 kg m^2 s^-1 (3.14 rad/s) = (125 kg m^2 s^-1 + 40.0 kg × 1.50 m^2)ω2
Solving for ω2 gives:
ω2 = 1.83 rad/s
Therefore, the answer is C.

A Playground Carousel Is Rotating About Its Center