A general question on finding the moment of inertia from oscillations.

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SUMMARY

The discussion centers on determining the moment of inertia of an object suspended from its center of mass, utilizing the radius of the string, the oscillation period, and the object's mass. The approach involves treating the object as a physical pendulum, where the small angle approximation (sinθ = θ) is applied for accurate calculations. Relevant resources include links to educational materials on simple harmonic motion and physical pendulums, which provide foundational knowledge for this analysis.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Knowledge of physical pendulum dynamics
  • Familiarity with the small angle approximation
  • Basic principles of rotational inertia
NEXT STEPS
  • Study the equations governing physical pendulums
  • Learn how to derive the moment of inertia from oscillation data
  • Explore the application of the small angle approximation in oscillatory systems
  • Investigate experimental methods for measuring moment of inertia
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Physics students, educators, and engineers interested in mechanics, particularly those focusing on oscillatory motion and rotational dynamics.

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Is there a way to find the moment of inertia of an object that is hung from its center of mass, knowing the radius of the string, the period of the oscillation, and the mass of the object? I've been trying to think of how to do this and I don't even know where to start.
 
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If the object is hung from its center of mass then you're talking about a pendulum but I think you had some other kind of oscillation in mind?
 
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/SHM/PhysicalPendulum.html
http://www.uccp.org/docs/Lab%20Facilitator%20Manuals/Honors_Physics/HonPhys_Lab07_Pendulum.pdf
http://www.phy.duke.edu/~rgb/Class/phy51/phy51/node23.html

The big assumption is that the initial displacement is relatively small,
i.e. sinθ = θ.
 
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