Angular Momentum: Solving Homework Confusion

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Angular momentum is a key concept in solving problems related to rotational motion, particularly when it comes to calculating final angular velocity. The relationship between kinetic energy and angular momentum is highlighted through the equations KE(rotational) = 1/2Iw^2 and Angular momentum = Iw. In this context, only angular momentum is conserved, which simplifies the calculations. Understanding that conservation of angular momentum allows for changes in kinetic energy to be related to final angular velocity is crucial. Clarity on these principles can resolve confusion in homework problems involving angular momentum.
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Homework Statement



I am just confused about Angular momentum.

Homework Equations

KE(rotational)= 1/2Iw^2
Angular momentum= Iw

The Attempt at a Solution



Why can I do the change in KE rotational to calculate the her final angular velocity in 3 revs?
very confused! :( both equations relate to moment of inertia and angular velocity.

Homework Statement


Homework Equations


The Attempt at a Solution

 

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Only angular momentum is conserved here. That's all you need.
 
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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