Acceleration in non-uniform circular motion

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SUMMARY

In non-uniform circular motion, such as a pendulum, centripetal acceleration cannot be zero, as it is essential for maintaining circular motion. If centripetal acceleration were zero, the centripetal force would also be zero, causing the object to cease its circular path. Tangential acceleration, however, can be zero at the peak positions of the pendulum where the speed is momentarily zero. Therefore, in the context of a frictionless piece of ice in a semi-circular bowl, it experiences non-zero centripetal acceleration at all times and zero tangential acceleration only at its peak positions.

PREREQUISITES
  • Understanding of centripetal acceleration and force
  • Knowledge of tangential acceleration and its relation to speed
  • Familiarity with the dynamics of pendulums
  • Basic principles of circular motion
NEXT STEPS
  • Study the equations governing centripetal acceleration in circular motion
  • Explore the relationship between tangential acceleration and speed changes in pendulums
  • Investigate the dynamics of frictionless motion in curved paths
  • Learn about the forces acting on objects in non-uniform circular motion
USEFUL FOR

Students of physics, educators teaching circular motion concepts, and anyone interested in the dynamics of pendulums and non-uniform circular motion.

nashsth
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In a non-uniform circular motion (for example a pendulum), can the centripetal/radial acceleration ever be 0? Likewise, can the tangential acceleration ever be 0?

The centripetal acceleration occurs because of the centripetal force, which causes the body (in the example of the pendulum, the bob is the body) to continue moving in its path. So if the centripetal acceleration is 0, then doesn't that imply that the centripetal force is 0, which means that the object would stop going in a circular path? So is it correct to say that the centripetal acceleration is never 0 in a non-uniform circular motion?

As for the tangential acceleration, it is caused by a change in speed of the body. So, in the pendulum example, since the bob has 0 speed at its peak positions, would it have 0 tangential acceleration only at its peak positions? NOTE: Peak position = the maximum position that a pendulum will attain before swinging down again.

I am asking because I am having trouble figuring out a (simple) physics question, which asks at which positions a frictionless piece of ice moving in a semi-circular bowl have 0 centripetal acceleration, but non-zero tangential acceleration. So if I am correct, then that would mean that the piece of ice has a non-zero centripetal acceleration at all times, and it has 0 tangential acceleration at its peak positions?
 
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