Problem Understanding Physical Pendulum

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SUMMARY

The discussion centers on understanding the variable 'h' in the equation for the period T of a physical pendulum, specifically a uniform circular disk with a radius of R=2.35cm and a pivot distance D=1.75cm from the center. The equation T=2π√(I/mgh) is analyzed, where I is the moment of inertia, m is mass, g is acceleration due to gravity, and h is the height. The user initially misinterprets h as the total height (h=D+R) but later clarifies that h should represent the distance from the pivot to the center of mass (COM) of the disk. The correct interpretation is crucial for accurate calculations of the pendulum's period.

PREREQUISITES
  • Understanding of physical pendulum dynamics
  • Familiarity with the parallel-axis theorem
  • Knowledge of moment of inertia calculations
  • Basic principles of simple harmonic motion (SHM)
NEXT STEPS
  • Review the derivation of the period of a physical pendulum
  • Study the parallel-axis theorem in detail
  • Learn about the moment of inertia for various shapes
  • Explore the effects of pivot placement on pendulum motion
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Students and educators in physics, mechanical engineers, and anyone studying dynamics and oscillatory motion will benefit from this discussion.

Saladsamurai
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I am having trouble understanding what h is in the equation for T listed below. Here is an image
th_Photo1.jpg
The Problem: A physical pendulum consists of a uniform circular disk (of R=2.35cm) supported in a vertical plane by a pivot located a distance D=1.75cm from the center of the disk. The disk is displaced by a small angle and released. What is the period T of the resulting SHM?

Equations:
[tex]T=2\pi\sqrt{\frac{I}{mgh}}[/tex]

[tex]I=I_{cm}+mH^2[/tex]

from text [tex]I_{disk}=\frac{1}{2}MR^2[/tex]

This is where I am messing up either my algebra or what I am interpreting as h.

For the parellel-axis theorem I had [tex]I_{disk}=\frac{MR^2}{2}+MD^2[/tex] where D is the distance from the COM to the pivot.

and for h in mgh I thought the total height was h=D+R.

Am I correct about what h is? Or no? This will determine what my mistake is

Thanks
Casey
 
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Don't worry...I got it.
 
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