Finding the Period of a Physical Pendulum Attached to a Solid Sphere

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SUMMARY

The discussion focuses on calculating the period of a physical pendulum consisting of a solid sphere with radius R, pivoted at its surface. The key conclusion is that the length of a simple pendulum that matches the period of this physical pendulum can be expressed in terms of R. The formula derived indicates that the effective length of the simple pendulum is related to the radius of the sphere, allowing for precise calculations in physics applications.

PREREQUISITES
  • Understanding of physical pendulum dynamics
  • Knowledge of simple harmonic motion
  • Familiarity with the concept of period in oscillatory systems
  • Basic geometry related to spheres and pendulums
NEXT STEPS
  • Research the formula for the period of a physical pendulum
  • Learn about the dynamics of solid spheres in rotational motion
  • Explore the relationship between amplitude and period in pendulum systems
  • Study the derivation of the effective length of a pendulum
USEFUL FOR

Students of physics, educators teaching mechanics, and engineers involved in pendulum design or analysis will benefit from this discussion.

jboone88
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I can't figure this one out:

A point of the surface of a solid sphere (radius = R) is attached directly to a pivot on the ceiling. The sphere swings back and forth as a physical pendulum with a small amplitude. What is the length of a simple pendulum that has the same period as this physical pendulum? Give answer in terms of R.

Thanks for the help
 
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