What Causes the Centripetal Acceleration in Circular Motion?

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Discussion Overview

The discussion revolves around the nature of centripetal acceleration in circular motion, specifically addressing why this acceleration is directed towards the center of the circle rather than in the direction of the velocity vector. Participants explore the mechanics of a marble inside a test tube being swung in a circular path, examining the forces at play during the motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that centripetal acceleration should align with the velocity vector, questioning why it points inward instead.
  • One participant describes a scenario involving a marble in a test tube, emphasizing that the marble initially moves in a straight line until the tube exerts a force on it.
  • Another participant mentions that when the marble reaches the end of the tube and moves in uniform circular motion, its acceleration must be centripetal due to the change in direction of the velocity vector.
  • There is a discussion about the nature of forces acting on the marble, with some asserting that the only force acting initially is tangential, while radial acceleration becomes relevant when the marble is constrained by the tube.
  • Participants express that radial acceleration arises because the marble's inertia wants to maintain a straight-line path, but the tube applies a force that alters this motion.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the marble's motion and the forces acting on it, particularly regarding the timing and nature of tangential versus radial acceleration. The discussion remains unresolved with multiple competing perspectives on the mechanics involved.

Contextual Notes

Some assumptions about the forces acting on the marble and the conditions under which the acceleration changes are not fully explored, leading to potential gaps in understanding the transition from tangential to radial acceleration.

cragar
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It seems that centripetal acceleration should be in the same direction as the velocity vector.
Why is it directed into the center of the circle. I remember walter lewin talking about a marble inside a glass test tube. Imagine the marble inside of it and I swing the test tube like a baseball bat horizontal to the ground. When i first start to swing the bat i push the marble with the side of the test tube and the marble wants to go in a straight line, and the reason it goes out towards the end is because when i move the test tube, I have allowed the marble moving in a straight line to occupy the end of the test tube. So why is the acceleration into the center of the circle.
 
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cragar said:
It seems that centripetal acceleration should be in the same direction as the velocity vector.
Once the marble has reached the end of the tube and is executing uniform circular motion, what is its acceleration? Compare how the velocity vector changes from moment to moment and you'll see why the acceleration is centripetal.
 
ok i see thanks for your response .
 
cragar said:
When i first start to swing the bat i push the marble with the side of the test tube and the marble wants to go in a straight line, and the reason it goes out towards the end is because when i move the test tube, I have allowed the marble moving in a straight line to occupy the end of the test tube. So why is the acceleration into the center of the circle.

hi cragar! :smile:

no, before the marble reaches the end, the only force is tangential (from the side of the tube), so the acceleration is purely tangential …

the radial acceleration is r'' - v2/r, and that has to be zero!

the radial acceleration doesn't become non-zero until there's a force from the end of the tube (forcing r'' = 0, of course) :wink:
 
so is the radial acceleration produced because the marble wants to move in a straight line but the end of the tube is pushing on it?
 
cragar said:
so is the radial acceleration produced because the marble wants to move in a straight line but the end of the tube is pushing on it?

acceleration can only be produced by a force …

the only force is from the glass of the tube …

initially it's tangential, but yes when the marble gets to the end it's radial :smile:

(and forget about where "the marble wants to move" … that's its present velocity, whcih has nothing to do with acceleration)
 
ok i think i got it , thanks for your answers
 
cragar said:
so is the radial acceleration produced because the marble wants to move in a straight line but the end of the tube is pushing on it?
Yes.
 

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