General question about center of mass

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Discussion Overview

The discussion revolves around the concept of the center of mass (CM) of a uniform ring, particularly in different contexts such as being suspended above the Earth and in space. Participants explore how the CM is determined and its implications for gravitational calculations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that the CM of a uniform ring is located at its center, regardless of its position.
  • Others question whether the attachment method (strings vs. rods) affects the CM, suggesting that it might change under different conditions.
  • One participant notes that the effective gravitational center of mass would only be at the center of the ring when observed from an infinite distance away.
  • There is a discussion about the limitations of using the CM for gravitational calculations, with some participants arguing that the gravitational field of an extended object cannot be simplified to that of a point mass at the CM.
  • An example involving the Earth and Moon is provided to illustrate that gravitational effects depend on the proximity of masses, indicating that the CM does not always dictate the direction of gravitational attraction.

Areas of Agreement / Disagreement

Participants generally agree that the CM of the ring is at its center, but there is disagreement regarding the implications of this for gravitational calculations and whether the CM can be treated as a point mass in certain scenarios.

Contextual Notes

Some participants highlight that the gravitational field of a ring cannot be approximated as that of a point mass, particularly when considering the distribution of mass and distance from the observer.

frozenguy
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I hope this is the right section.

consider the CM of a uniform ring. Suspend that ring by light cables above the earth, by a crane maybe?

Where is the rings center of mass now? If this system was in space (crane, cables, ring), the CM would be somewhere else right?

If the ring was out in space, and had a satellite orbiting its CM, and I come up to it and touch the ring, won't the satellite adjust its orbit?
 
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frozenguy said:
consider the CM of a uniform ring. Suspend that ring by light cables above the earth, by a crane maybe?

Where is the rings center of mass now? If this system was in space (crane, cables, ring), the CM would be somewhere else right?
The CM of the ring is right at its center.

If the ring was out in space, and had a satellite orbiting its CM,
What do you mean? For the purposes of calculating gravitational forces, you can't treat the ring as if its mass were concentrated at its CM, if that's what you're thinking.
 
The effective gravitational centre of mass would only be at the centre of the ring if observed from an infinite distance away.
 
Doc Al said:
The CM of the ring is right at its center.
Is that because they are strings attaching the ring to the crane? If it were light rods, then the CM would change right?


Doc Al said:
What do you mean? For the purposes of calculating gravitational forces, you can't treat the ring as if its mass were concentrated at its CM, if that's what you're thinking.

Why can't you use the CM for gravitational calculations?
 
frozenguy said:
Is that because they are strings attaching the ring to the crane? If it were light rods, then the CM would change right?
Why would it change? Think of the CM as being the average location of the object's mass. The CM of the ring will always be right at its center.

Why can't you use the CM for gravitational calculations?
That's only good when the object can be treated as a point mass (for example, if you are very far away from it, as sophiecentaur said) or if it has a spherically symmetric mass distribution. In general, the gravitational field of an extended object can only be found by adding up the field from each of its pieces. In the case of a ring, that field will not look like the field of a point mass located at the ring's center.
 
frozenguy said:
Why can't you use the CM for gravitational calculations?

To answer that question consider this example. The Centre of Mass of the Earth and Moon is somewhere below the Earth's surface. If you are standing on the Moon and you drop a hammer, it falls towards your feet - not towards the centre of mass of Moon and Earth. The nearby(smaller) mass of the Moon counts more than the distant Centre of Mass in that particular gravitational calculation.
 

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