What is the arc length of a pendulum bob with mass m and length l?

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SUMMARY

The arc length of a pendulum bob with mass m and length l, when displaced through an angle θ, is calculated using the formula arc length = θ * l. However, the challenge arises when the angle of displacement θ is unknown, as it is a variable in the expression. This discussion highlights the need to determine θ to accurately compute the arc length of the pendulum's motion.

PREREQUISITES
  • Understanding of basic trigonometry
  • Familiarity with pendulum mechanics
  • Knowledge of angular displacement
  • Concept of arc length in circular motion
NEXT STEPS
  • Research methods to measure angular displacement in pendulum systems
  • Explore the relationship between angle and arc length in circular motion
  • Study the dynamics of pendulum motion under varying angles
  • Learn about the effects of mass on pendulum behavior
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of pendulum systems will benefit from this discussion.

william kat
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a pendulum bob of mass m hangs on a string of length l. what is the espression for the arc length of the bob if its discplaced through an angle theta.
 
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well if you know the maximum angle of displacement the arc length is simply

theta*l
 
problem is, the angle of discplacement is not known. its part of the expression
 

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