Moment of Inertia - Hollow Objects

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SUMMARY

The discussion focuses on calculating the moment of inertia for a thin conical shell and a partially hollowed thick uniform spherical shell. The moment of inertia for the conical shell about its center of mass is derived using the parallel axis theorem, with the known moment of inertia of 19/4 ma² about the apex. For the spherical shell, the moment of inertia about a diameter is determined from its known value of 23/15 ma² about a tangent. These calculations are essential for understanding rotational dynamics in physics.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with the parallel axis theorem
  • Knowledge of rotational dynamics
  • Basic proficiency in calculus for integration (if needed)
NEXT STEPS
  • Study the parallel axis theorem in detail
  • Learn about the moment of inertia for various geometric shapes
  • Explore applications of moment of inertia in rotational motion problems
  • Review advanced topics in rotational dynamics, including torque and angular momentum
USEFUL FOR

Students preparing for physics exams, educators teaching mechanics, and anyone interested in the principles of rotational dynamics and moment of inertia calculations.

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:
 

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