Comparing moment of inertia to mass in linear motion

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The discussion focuses on comparing the roles of moment of inertia in rotational motion and mass in linear motion. Moment of inertia is essential for understanding rotational dynamics, similar to how mass influences linear dynamics through force, acceleration, momentum, and kinetic energy. Participants emphasize the importance of grasping the definitions and applications of these concepts rather than merely seeking direct answers. The conversation encourages a deeper comprehension of how moment of inertia is defined and utilized in physics. Ultimately, understanding these relationships is key to mastering both rotational and linear motion concepts.
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Homework Statement


Compare the role played by the moment of inertia in rotational motion, to that played by mass in linear motion.


Homework Equations


I have no idea how to tackle this question. I tried looking up the defenition of moment of inertia as a start, but I only found anything relevant in a linear momentum. How should I answer this please?


The Attempt at a Solution


Couldn't figure it out...
 
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Look at how mass is used in linear motion. Note it appears in defining the relationship between force and acceleration, between momentum and velocity, and in defining kinetic energy. Look at the corresponding relationships in rotational motion.

The question is designed to test your understanding. So while reading up on e.g. moment of inertia, don't look for the answer, look for understanding! How is moment of inertia defined and how is it used? (Note that in physics these are the same question! Don't confuse "how it is calculated" with "how it is defined"!)
 
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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