Circular Motion - Pendulum swinging

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SUMMARY

The discussion focuses on analyzing the motion of a pendulum swinging in a circular arc, specifically calculating the centripetal and tangential components of acceleration. Given a pendulum bob speed of 2.7 m/s and a length of 0.75 m at an angle of 15 degrees, the centripetal acceleration is calculated using the formula ac = v²/r. The maximum centripetal acceleration occurs when the pendulum is at its lowest point, while the tangential acceleration can be derived from the angular acceleration using at = rα.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with acceleration components in physics
  • Knowledge of pendulum mechanics
  • Proficiency in using trigonometric functions for angle calculations
NEXT STEPS
  • Calculate centripetal acceleration for various speeds using ac = v²/r
  • Explore the relationship between angular acceleration and tangential acceleration using at = rα
  • Investigate the effects of varying pendulum lengths on acceleration components
  • Learn about energy conservation in pendulum motion and its impact on speed and acceleration
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators looking for examples of pendulum dynamics in classroom discussions.

bahrmd
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Homework Statement


A pendulum swinging in a circular arc under the influence of gravity has both centripetal and tangential components of acceleration. (a) If the pendulum bob has a speed of 2.7m/s when the cord makes an angle of [tex]\Theta[/tex] =15 deg with the vertical, what are the magnitudes of the components at this time? (b) where is the centripetal acceleration a maximum? What is the value of the tangential acceleration at that location?

Length of the pendulum equals 0.75m

Homework Equations


ac=v^2/r

at=r[tex]\alpha[/tex]


The Attempt at a Solution



So I need to find the magnitude of ac, a, and at.

I have a Length, an angle, speed and gravity.

ac=2.7m/s^2/0.75
at=0.75(?)
a=?
 
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