General question about center of mass

[frozenguy]

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?

 

[Doc Al]

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.

 

[sophiecentaur]

The effective gravitational centre of mass would only be at the centre of the ring if observed from an infinite distance away.

 

[frozenguy]

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?

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?

 

[Doc Al]

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.

 

[sophiecentaur]

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.