Moment of Inertia - Hollow Objects

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The discussion revolves around calculating the moment of inertia for a thin conical shell and a partially hollowed thick spherical shell. The moment of inertia for the conical shell is given, and the task is to find it about an axis through its center of mass using the parallel axis theorem. For the spherical shell, the moment of inertia about a diameter needs to be determined, given its moment of inertia about a tangent. Participants are encouraged to apply relevant equations and theorems to solve these problems effectively. The thread emphasizes the importance of understanding the principles behind moment of inertia calculations for exam preparation.
JerS
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Homework Statement



1. Given that the moment of inertia of a thin conical shell, of base radius a and height 3a, about
an axis through its apex perpendicular to its symemtry axis is 19
4 ma2, and that the centre of
mass of the shell is along its symmetry axis a distance a from the base and 2a from the apex,
find the moment of inertial of the conical shell about an axis which passes through its centre
of mass and is perpendicular to its symmetry axis.
2. A partially hollowed out thick uniform spherical shell, of mass m and outer radius a, has
moment of inertia 23
15 ma2 about a tangent. What is the moment of inertia of the shell about a
diameter, given that its centre of mass is at the centre of the shell?


Homework Equations



I = Sigma m (r^2)



The Attempt at a Solution



Lots on paper



Thanks tons, again this is for an exam tomorrow
 
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Welcome to PF!

Hi JerS! Welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)

Hint: use the parallel axis theorem …

what do you get? :smile:
 
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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