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Old Jul 29th 2014, 01:24 PM   #1
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I am confused on the concept/definition for center of mass and center of gravity?

I am having trouble understanding the definition for center of mass and center of gravity.

In my book it says that the center of mass is the point at which we could consider all the mass of the object to be concentrated.

The center of gravity is the point at which the total gravitational force on the object can be considered to act.

I am not sure if this is the right thinking, but

I think that these definitions mean that given an object with a uniform density, not all of the parts that make up the object will have the full mass at a point away from its geocentric center or also full gravity for the same reason. For example, in a Bowling ball, the further out from the geocenter, the point or part of the ball will not be considered to have the full mass of the whole object as opposed to measuring the mass of the ball at the dead center. However, I am not sure how you would measure these to show that the side of the ball will have less mass.
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Old Jul 29th 2014, 02:26 PM   #2
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If an object has uniform density then the center of mass is the centroid of the object. In some cases you can consider the entire mass of an object concentrated at the CM for calculating answers to certain types of problems, but not all. For example - in calculating gravitational forces between two homogeneous spheres we use the equation:

F = GMm/r^2

where m and M are the masses of the two bodies and r is the distance between their centers (which is also where the sphere's centroid is located - and hence its center of mass as well). But for bodies that are not spherical or homogeneous the measurement of r is a bit more complicated, and in general you can't assume that r is measured from the centroids of the two bodies.

The center of gravity is the point about which there is no torque if the body is placed in a uniform gravitational field with parallel lines of force. If you tie a string to an object and suspend it, the object's CG will be at some point in line with the string. Do this experiment twice, using different points to suspend the object and the CG is at the intersection of the two lines. The idea behind CG is that you can solve physics problems involving effects of uniform gravity on an object and assume that the objects complete mass is at that point - but again, this works only for uniform gravitational fields with parallel lines of force - such as near the surface of the Earth.

An object's CM and CG are always at the same place. Hence we tend to use the terms interchangeably.

Hope this helps.
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Old Jul 30th 2014, 02:05 AM   #3
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To a certain extent the centre of mass is a bit of a mathematical shortcut.
If you were to (in imagination) divide up the shape into lots of little bits
and then add up all the individual effects of the mass of all the little bits
you would find that the answer would be exactly the same as if you had just assumed all the mass was located at one point.
This one point is called the center of gravity or (perhaps more correctly) the center of mass.
Once you have worked out the position of the centre of mass, any other calculations which depend on the mass become much easier.

Last edited by MBW; Aug 2nd 2014 at 02:54 AM.
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Old Jul 30th 2014, 11:36 AM   #4
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Thanks Mbw and ChipB! This really helped!
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