Box with a horizontal force at the top

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Discussion Overview

The discussion revolves around the behavior of a cubical box subjected to a horizontal force applied off-center. Participants explore the implications of this force on the box's motion, particularly focusing on rotation about the center of gravity and the associated physical principles.

Discussion Character

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

Main Points Raised

  • One participant questions why the box rotates about the center of gravity rather than another point, seeking a mathematical proof for this behavior.
  • Another participant explains that the off-center force leads to both linear acceleration of the center of mass and torque about the center of mass, resulting in angular acceleration.
  • A further contribution clarifies that while torque can be calculated about any point, using the center of mass simplifies the description of motion, as it separates translation from rotation.
  • It is noted that the object may not be in pure rotation about the center of mass, as the instantaneous axis of rotation can vary.

Areas of Agreement / Disagreement

Participants express differing views on the nature of rotation and the choice of the center of mass as a reference point. The discussion remains unresolved regarding the necessity of rotation about the center of gravity and the implications of using different points for torque calculations.

Contextual Notes

Limitations include the lack of a definitive mathematical proof for the rotation about the center of gravity and the dependence on the definitions of torque and rotation in the context of the discussion.

chandran
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Theory says that a cubical box when subjected to a force horizontally(not at the centre of gravity) then the force will tend to rotate the box around the centre of gravity. Any proof can be given for this?
 
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This is a consequence of Newton's laws of motion. The off-center force, assuming it's the only force acting, does two things:
(1) It accelerates the center of mass
(2) It exerts a torque about the center of mass, producing an angular acceleration
 
docal,
that is where i am asking. Why don't the box rotate about some other point. why it should rotate about cg. Any mathematical proof?

thanks.
 
I think I see what the issue is. Since torque can be found with respect to any point, then any point can be considered as an "axis of rotation". This is true. But for any point other than the center of mass you will be mixing up the translation with the rotation. So using the center of mass is for convenience in describing the motion: the motion of an object is the sum of the translation of its center of mass plus the rotation about the center of mass.

Note that this does not mean that the object is in pure rotation about the center of mass! The instantaneous axis of rotation (the point about which the object appears to be in pure rotation) can be anywhere.
 

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