Angular Momentum: Formula Comparison & Usage

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Two formulas for calculating angular momentum are discussed: L = r x p for point particles and L = Iw for objects rotating about a fixed axis. The first formula applies to point particles, while the second is suitable for extended objects, such as a rod rotating around one of its ends. It's important to ensure that the moment of inertia (I) corresponds to the object and axis in question. Understanding when to use each formula is crucial for accurate calculations. Proper application of these formulas is essential for analyzing angular momentum in various physical scenarios.
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I have two formulas to find angular momentum, and I am not sure when to use one and when to use the other, or what the difference is between the two. One is L = r x p, and the other is L=Iw.
 
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The former is used for a the angular momentum of point particle about some point, while the latter is used for the angular momentum of an object rotating about a fixed axis.
 
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ok, I understand now. Thanks
 
so, if it's a rod, for example, rotating about one of its ends, I should use L=Iw?
 
Given that a rod is not a point particle, yes.

Just be careful to note that the moment of inertia (I) you are using is for that object about the given axis.
 
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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