Non uniform circular motion acceleration

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Discussion Overview

The discussion revolves around the concept of acceleration in non-uniform circular motion, specifically focusing on how centripetal acceleration behaves when velocity changes while maintaining a constant radius.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that in uniform circular motion, acceleration can be calculated using the formula A = v²/r, but questions how this applies in non-uniform motion where velocity is changing.
  • Another participant suggests consulting the Frenet equations, which address the more general case of motion, including non-uniform circular motion.
  • A third participant provides a resource related to the application of the Frenet equations in two dimensions, indicating that the equations simplify in that context.
  • A participant reiterates their original question about whether centripetal acceleration will increase, emphasizing the condition of staying on the same circle of radius r.
  • A later reply affirms that if the object remains on the same circle, the centripetal acceleration will indeed increase as velocity changes.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between changing velocity and centripetal acceleration in non-uniform circular motion, with some asserting that centripetal acceleration increases under certain conditions while others seek clarification on the topic.

Contextual Notes

The discussion does not resolve the nuances of how centripetal acceleration varies with changing velocity, and assumptions regarding the nature of the motion and the radius are not fully explored.

ahmed emad
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In uniform curved motion , I can get the acceleration from the equation :
A = v2/r , but in non uniform the velocity is changing , so will the certipetal acceleration also change ?
 
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Google the Frenet equations. Those equations treat the more general case.
 
It's far from my question. I meant will the centripetal acceleration increase?
 
ahmed emad said:
It's far from my question. I meant will the centripetal acceleration increase?
If the object stays on the same circle of radius ## r ##, the answer is yes.
 
Okay , thanks very much.
 
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