Center of gravity & moment of inertia

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Discussion Overview

The discussion revolves around the relationship between center of gravity, moment of inertia, and stability when standing with legs spread apart. Participants explore how these concepts interact and whether they counteract each other in the context of physical stability and rotation.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant suggests that spreading legs lowers the center of gravity, which could reduce the moment of inertia, potentially making it easier to rotate.
  • Another participant argues that the effects of lowering the center of gravity and moment of inertia are perpendicular, implying that changing one does not affect the other.
  • A later reply elaborates that while spreading legs does help with stability by increasing the base, the relevant axis of rotation is not significantly affected by the change in stance, thus questioning the initial assumption about moment of inertia.
  • Another participant points out that the moment of inertia is influenced by the distance of body parts from the axis of rotation, using the analogy of figure skaters to illustrate how changing arm positions affects spin speed without altering the center of gravity.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between center of gravity and moment of inertia, with no consensus reached on whether spreading legs affects these properties in a counteractive manner.

Contextual Notes

Participants note that the effects of spreading legs on stability and rotation may depend on the specific axis of rotation considered, which remains unresolved in the discussion.

godingly
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Dear forum,
while standing, spreading your legs helps your stability because you have a wider base.
but doesn't spreading your legs lowers your center of gravity, thus shortening the distance (r) from your center of gravity to the ground, and therefore lowering your moment of inertia = making you easier to rotate?

The two seems to me to counteract. is that right?
 
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The two effects, lowering c.g. and moment of inertial around a vertical axis (for rotation) are perpendicular, so changing one doesn't effect the other.
 
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godingly said:
Dear forum,
while standing, spreading your legs helps your stability because you have a wider base.
but doesn't spreading your legs lowers your center of gravity, thus shortening the distance (r) from your center of gravity to the ground, and therefore lowering your moment of inertia = making you easier to rotate?

The two seems to me to counteract. is that right?

The effect of spreading your legs is static. If someone is trying to tip you over toward the right, the fact that your right foot is farther right means that 1) they have farther to push to get you past the tipping point and 2) gravity has a longer moment arm to resist the tipping torque.

The effect of lowing your center of gravity is dynamic. If you assumed that the axis of rotation were on the ground below your center of gravity then widening your stance and the resultant lowering of your center of gravity could reduce your moment of inertia. But that is not where the relevant axis of rotation is located. If someone is trying to tip you over to the right, your right foot is the relevant axis of rotation. Adopting a wider stance does not move your right foot much closer to your center of gravity.
 
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Spreading legs does affect your moment because part of you is moving away from the axis, not because you are lowering your body. Think of figure skaters moving arms in and out. the center of gravity is unaffected, but the moment changes, so they spin faster when the arms are closer to their bodies.
 

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