Hey I need some help with this physics home work problem. It isphysics (8th) Cut

Question

Hey I need some help with this physics home work problem. It isphysics (8th) Cutnell. Chapter 9 problem 61. It reads asfollows:

-A playground carousel is rotating counterclockwise about itscenter on frictionless bearings. A person standing still on theground grabs onto one of the bars on the carousel very close to itsouter edge and climbs aboard. Thus, this person begins with anangular speed of zero and ends up with a nonzero angular speed,which means that he underwent a counterclockwise angularacceleration. The carousel has a radius of 1.53 m, an initialangular speed of 3.21 rad/s, and a moment of inertia of 120kg·m2. The mass of the person is 42.2 kg. Findthe final angular speed of the carousel after the person climbsaboard.

Thanks!!

Explanation / Answer

consider a system consisting of the person and the carousel. Since the carousel rotates on frictionless bearings, no netexternal torque acts on this system. Therefore, angularmomentum is conserved, and we can set the total angular momentum ofthe system before the person hops on equal to the total angularmomentum afterwards. Afterwards, the angular momentum includesa contribution from the person.   his moment ofinertis = Iperson = MR2, since he is atthe outer edge of the carousel.                              Icarsouel f + Iperson f = Icarousel o                                 f= Icar o/Icar +MR2                                       = 120kg/m2 (3.14rad/s)/120kg.m2 + (42.2kg )(1.53m)2                                      = ----------rad/s                                      = ----------rad/s

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