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of a body?is it necessary that all the points coincide?

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- Thread starter monty37
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- #1

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of a body?is it necessary that all the points coincide?

- #2

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Those all mean the same thing.

- #3

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of a body?is it necessary that all the points coincide?

Take a triangle for example.

The centroid is the mean position of elements of area.

The centre of mass is the mean position of elements of mass.

In a uniform gravitaional field, the force of gravity on the triangle

can be taken as acting through the centre of mass.

But if the mass per unit area of the triangle varied, the centre of mass

would not (usually) coincide with the centroid.

Note also that the assumption that the earth's gravity is the same

as if its mass were all located at the centre is only true because of

its spherical symmetry.

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HallsofIvy

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With a gravity field that falls off linearly with distance, center of mass and center of gravity are the same. However, with a gravity field that falls off with the inverse square of distance, center of gravity and center of mass are not the same. For a small object, say something the size of the space station, the difference between center of mass and center of gravity is very small because the first order linear approximation is very, very good.

For a large object, say something the size of a space elevator, center of mass and center of gravity are very different. Lay literature on a space elevator often claim the center of mass needs to be at geostationary altitude. This is incorrect. It is the center of gravity that needs to be at geostationary altitude. The center of mass needs to be well above geostationary altitude.

- #6

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for the earth as such ,a sphere,all the three points coincide ,right?

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