Normal reaction in a rolling object

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Discussion Overview

The discussion revolves around the normal reaction force acting on a rolling object, particularly in the context of a sphere rolling down an incline. Participants explore the representation of the normal force in diagrams and its implications for understanding the forces at play in rolling motion.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question why the normal reaction force is depicted to the side of the center of mass (CM) in diagrams, suggesting it may imply a misunderstanding of its actual application.
  • Others clarify that the normal force is shown to the side for clarity in diagrams, indicating that it acts through the center of mass and does not actually act off to the side.
  • A participant provides a detailed explanation of the forces acting on a solid sphere rolling down an incline, including the gravitational force and the normal force, while emphasizing the role of the force at the point of contact in accelerating the sphere's rotation.
  • Some participants reference external resources to support their points, indicating that the normal and gravitational forces do not affect the motion because their line of action passes through the center of rotation.

Areas of Agreement / Disagreement

Participants express differing views on the representation of the normal force in diagrams, with some asserting that it is misleading while others defend the clarity of the representation. The discussion remains unresolved regarding the implications of the normal force's depiction.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the forces acting on the rolling object and the dependence on the specific definitions of the forces involved. The mathematical steps related to the forces and their effects on motion are not fully resolved.

vin300
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Why is the normal reaction to a rolling object shown to the side of the CM?
Forces must be equal and opposite
Is there a real problem if you assume it through the C?
 
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What exactly are you talking about? The normal force exerted by the surface of an incline on a sphere rolling down it? If so, why do you say that the normal force is shown "to the side of the CM"?
 
I thought this should be clear
Thishttp://webphysics.davidson.edu/faculty/dmb/py430/friction/rolling.html"
 
Last edited by a moderator:
vin300 said:
I thought this should be clear
Thishttp://webphysics.davidson.edu/faculty/dmb/py430/friction/rolling.html"
In the first two diagrams, the normal force arrow is shown to the side just for clarity. (Otherwise it would be right on top of the weight force arrow.) There's no implication that the normal force actually acts off to the side.
 
Last edited by a moderator:
:smile:
 
Maybe this will help. If a solid sphere of radius R and moment of inertia I = (2/5) m R2 is rolling (without slipping) down a slope of angle theta, then the accelerating force (parallel to the slope) on the sphere at its center of mass is mg sin(theta). But there is an uphill force at the point of contact with the slope (not at the sphere's center of mass) that is accelerating the rotation of the sphere. Also, for completeness, the normal (perpendicular) force of the sphere against the slope is mg cos(theta).
 
vin300 said:
I thought this should be clear
This http://webphysics.davidson.edu/faculty/dmb/py430/friction/rolling.html"
Just under the diagram is this text:

( The normal and gravitational forces produce no effect because their line of action is through the center of rotation. )

So although the diagram has the normal vector drawn a bit to side, it actually goes through the center of mass.
 
Last edited by a moderator:

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