Classical mechanics: centripetal acceleration

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Discussion Overview

The discussion revolves around the concept of centripetal acceleration, particularly in the context of an object moving in a vertical circle. Participants explore the conditions necessary for maintaining tension in a string and the relationship between speed, acceleration, and gravitational forces at the top of the circular path.

Discussion Character

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

Main Points Raised

  • One participant questions why an object must have centripetal acceleration greater than 'g' to reach the top of a vertical circle and what happens if it has just enough speed to reach the top.
  • Another participant suggests analyzing the forces acting on the object at the top of the circle to determine the minimum speed required for non-zero tension in the string.
  • Some participants discuss the concept of centrifugal force and its relevance, with one arguing that it is unnecessary to introduce this concept when using an inertial reference frame.
  • One participant derives an equation relating tension, gravitational force, and acceleration, concluding that centripetal acceleration must be greater than 'g' for the string to remain taut.
  • Another participant points out that the acceleration referred to in the equation is linear acceleration, which may lead to confusion in the context of centripetal motion.
  • Several participants discuss the relationship between centripetal acceleration and speed, with one suggesting substituting the expression v²/r for acceleration to find the minimum speed required.

Areas of Agreement / Disagreement

Participants generally agree on the need for centripetal acceleration to be greater than 'g' for the string to remain taut, but there is some confusion regarding the calculation of minimum speed and the interpretation of forces involved. Multiple views on the necessity of centrifugal force are present, indicating a lack of consensus on that aspect.

Contextual Notes

Some participants express uncertainty about the calculations involved in determining minimum speed and the definitions of forces at play, highlighting potential limitations in their understanding of centripetal motion.

Who May Find This Useful

This discussion may be useful for students or individuals interested in classical mechanics, particularly those studying circular motion and the forces involved in maintaining such motion.

Parallel
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I need some help with centripetal acceleration.

why when an object is whirling in a vertical circle,it must have a centripetal acceleration larger than 'g' in order for it to get to the top of the circle?

what if I give it just enough speed to get to the top(so when it gets to the top,it's speed is zero)will it fall straight down,or will it just "go back"?

it's really hard for me to conceptualize that

thank you in advance
 
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Take a ball whirling on a string as an example. To maintain a vertical circle, the string must be taut at all times. Analyze the forces acting on the ball when at the top of the circle. To just barely have non-zero tension in the string, what's the minimum speed required according to Newton's 2nd law?
 
For an object to stay in circular motion it must have a force keeping it from flying away. this is the centrifugal force. for example, in the case of a ball on a string the centrifugal force is equal to the tension on the string. so the C force is non 0 even without gravity. with gravity it just has to be bigger.
 
daniel_i_l said:
For an object to stay in circular motion it must have a force keeping it from flying away. this is the centrifugal force. for example, in the case of a ball on a string the centrifugal force is equal to the tension on the string. so the C force is non 0 even without gravity. with gravity it just has to be bigger.
If one considers the situation properly, from an inertial reference frame, there is no need to introduce an imaginary centrifugal force; one should use centripetal force in order to avoid confusion.
 
So if I look at the forces acting on the object when it's at the top of the circle ,I get that: the string is pulling it down
and the gravitational force is pulling it down

so: T+mg = ma

T = m(a-g)

so the acceleration must be greater than 'g' ,if I want the string to be taut!.
this is the centripetal acceleration, and this is why it must be larger than 'g'.

Am I getting this right?

I'm not so sure how to caclulate the minumum speed required.
 
Your getting close, but the a in your equation above indicates linear acceleration, which is not what you want. The important thing to remember here is that at minimum speed the sum of the forces must be equal to the centripetal force.
 
Parallel said:
So if I look at the forces acting on the object when it's at the top of the circle ,I get that: the string is pulling it down
and the gravitational force is pulling it down

so: T+mg = ma

T = m(a-g)

so the acceleration must be greater than 'g' ,if I want the string to be taut!.
this is the centripetal acceleration, and this is why it must be larger than 'g'.

Am I getting this right?
Yes, everything you said is correct.

I'm not so sure how to caclulate the minumum speed required.
Use what you know about centripetal acceleration. How does centripetal acceleration relate to speed?
 
So should I just substitute v^2/r for a?

About the minumum speed,I'm still not getting it.
 
Yes, use that expression for centripetal acceleration. Since you know the minimum acceleration, you can solve for the corresponding minimum speed.
 
  • #10
I got it.

I want to thank you all for your help,thank you.
 

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