Tangential Acceleration of a Pendulum

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SUMMARY

The discussion focuses on calculating the tangential acceleration of a pendulum bob with a mass of 2 kg and a string length of 2 meters, released at a velocity of 1.5 meters/second from a 30-degree angle. The correct tangential acceleration at the highest point of motion is established as 5.77 meters/second squared. Participants emphasize the importance of considering both kinetic and potential energy to determine the maximum height and the corresponding angle, which directly influences the tangential acceleration due to gravity.

PREREQUISITES
  • Understanding of pendulum dynamics
  • Familiarity with gravitational potential energy and kinetic energy concepts
  • Knowledge of basic trigonometry for angle calculations
  • Ability to analyze free body diagrams (FBD)
NEXT STEPS
  • Study the principles of energy conservation in pendulum motion
  • Learn how to calculate maximum height using gravitational potential energy
  • Explore the relationship between angular velocity and tangential acceleration
  • Review the derivation of tangential acceleration formulas in rotational dynamics
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of pendulum motion and the calculations involved in determining tangential acceleration.

Sandman327
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Homework Statement


A 2kg pendulum bob on a string 2 meters long is released with a velocity of 1.5 meters/second when the support string makes an angle of 30 degrees with the vertical. What is the tangential acceleration of the bob at the highest point of its motion? The answer was given as 5.77 meters/second squared so I know that that is the answer but it's getting to that number that is giving me tons of trouble.


Homework Equations


Tangential acceleration = r(delta omega/change in time)


The Attempt at a Solution

I have an FBD and the only force acting on the bob is gravity. However the problem I'm having is that I am almost positive there is another equation I should be using but I'm not sure what it is or what I should try to solve for. Time? Maximum height? both?
 
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Consider the total energy of the system.

They give you the kinetic energy. You have the potential energy from gravity with reference to how high it is from the bottom. So figure the maximum height first, and then figure what angle that makes, and that angle to gravity is the fraction of gravity which is the tangential acceleration I think they are looking for.
 

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