Merry-go-round => what is conserved?

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In the discussion about a boy jumping onto a merry-go-round, the key focus is on which physical quantities are conserved. The boy's initial linear momentum is affected by the force from the merry-go-round's hub, while angular momentum remains conserved due to the system's rotational nature. Participants debate whether both linear and angular momentum are conserved or just angular momentum, with the consensus leaning towards only angular momentum being conserved due to the inelastic nature of the collision. Kinetic energy is not conserved in this scenario, reinforcing the idea that angular momentum is the primary conserved quantity. The conclusion emphasizes that only angular momentum is conserved in this situation.
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A boy of mass m = 40 kg running with speed v = 4 m/s jumps onto the outer edge of a merry-go-round of mass M = 160 kg and radius R = 1.8 m, as shown in the picture above. The merry-go-round is initially at rest, and can rotate about a frictionless pivot at its center. You may assume that the inital velocity of the boy is tangent to the edge of the merry-go round.

Which of the following quantities are conserved throughout this problem for the system consisting of the boy and the merry-go-round?

A) only kinetic energy
B) kinetic energy and angular momentum
C) only linear momentum
D) linear momentum and angular momentum
E) only angular momentum

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I believe the answer is D, linear momentum AND angular momentum because both are conserved regardless of an inelastic or elastic collision right?

::
Can somebody please check out my answer and help me if it is wrong? Thank you very much in advance.
 
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Wait, wouldn't only the angular momentum be conserved since the boy's velocity changes after contact with the merry-go-round?

So only the angular momentum is conserved?
 
It's an inelastic collision, so there's goes thinking kinetic energy would be conserved.

For linear momentum, when the boy contacts the rim of the go-round there is a force coming from the hub that resists the linear motion, but not the angular momentum. I think your choice of angular momentum only would be the correct answer.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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