What Determines the Period of a Physical Pendulum?

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SUMMARY

The period of a physical pendulum can be calculated using the formula T = 2π√(I/mgh). In this discussion, a physical pendulum with a mass of 4.4 kg and a moment of inertia of 33.9 kg-m² about its center of mass was analyzed. The suspension point was 276.69 cm from the center of mass, leading to a calculated period of T = 3.35 seconds. The correct application of the formula, considering the inertia about the suspension point rather than the center of mass, confirmed the accuracy of the solution.

PREREQUISITES
  • Understanding of physical pendulum dynamics
  • Knowledge of moment of inertia calculations
  • Familiarity with gravitational acceleration (g = 9.81 m/s²)
  • Ability to manipulate and solve algebraic equations
NEXT STEPS
  • Study the derivation of the physical pendulum period formula
  • Explore the effects of varying mass and moment of inertia on pendulum behavior
  • Learn about the relationship between suspension point and center of mass in pendulum systems
  • Investigate real-world applications of physical pendulums in engineering and design
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Students studying physics, particularly those focusing on mechanics, as well as educators and anyone interested in the principles of pendulum motion and dynamics.

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Homework Statement



A physical pendulum is constructed using a 4.4 kg object having a moment of inertia of 33.9 kg-m2 about its center of mass. The rotation (suspension) point is 276.69 cm from the center of mass. What is the period of this physical pendulum?


Homework Equations



T = 2pi sq rt (I/mgh)

The Attempt at a Solution



Every attempt at this problem yields T = 3.35s. I did a little research to make sure I was using the correct equation, but I didn't find anything to contradict what I'm using. Inertia is kg-m^2; m=4.4kg, g=9.81m/s^2, and h=2.7669m. Any help is appreciated.
 
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Note that I must be about the suspension point, not the center of mass.
 
Doc Al said:
Note that I must be about the suspension point, not the center of mass.

That's it! I worked out the problem using I about the suspension point and it's correct. Thank you for the insight.
 

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