How is the moment of inertia related to the square of the distance?

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Discussion Overview

The discussion revolves around the relationship between moment of inertia and the square of the distance from the axis of rotation. Participants explore the implications of mass and distance on moment of inertia, particularly in the context of rotational dynamics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants state that moment of inertia is defined as I = MR², indicating a direct proportionality to mass and the square of the distance.
  • Others clarify that this relationship holds for point masses and is contingent on the distance to the axis being fixed.
  • One participant notes that moment of inertia measures the torque required for a given rotational acceleration, suggesting that greater distance from the axis increases the difficulty of rotation.
  • Repeated inquiries are made regarding why the relationship involves the square of the distance rather than a linear relationship.
  • A participant provides a link to an external resource for further exploration of the topic.

Areas of Agreement / Disagreement

Participants express uncertainty about the reasoning behind the square of the distance in the moment of inertia formula. There is no consensus on this aspect, and multiple viewpoints are presented without resolution.

Contextual Notes

Participants do not fully address the underlying assumptions or definitions related to moment of inertia, particularly in varying contexts beyond point masses.

Hardik Batra
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Moment of inertia is
I = MR2
object has more mass means more inertia and less mass means less inertia.
That means moment of inertia is directly proportional to mass.
But how the moment of inertia is directly proportional to the square of the distance.?
 
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Hardik Batra said:
Moment of inertia is
I = MR2
For a point mass, not in general.

Hardik Batra said:
object has more mass means more inertia and less mass means less inertia.
OK.

Hardik Batra said:
That means moment of inertia is directly proportional to mass.
Only if the distance to the axis--the R--is fixed.

Hardik Batra said:
But how the moment of inertia is directly proportional to the square of the distance.?
It's a measure of the torque required to produce a given rotational acceleration. Loosely: The further the mass is from the axis, the harder it is to get it to rotate.
 
but why it is square of the distance rather than only distance.
 
Thanks. It helpful for me.
 

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