my question is basically whether centre of mass is a theoretical concept. As an example, say for a ruler we say that the centre of mass is in the middle and i get that completely, however for something like a ring the centre of mass is in the middle where there is no mass. Now this confuses how the centre of mass can be at a location where there is no mass at all which leads me to think its a theoretical concept. Is my understanding correct?

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    $\begingroup$ In the same way that the average need not be a possible outcome: If you have a dime and a penny on average you will draw 5.5 cents, even if none of your coins has that value. $\endgroup$ – ZeroTheHero Apr 4 '17 at 0:22

The center of mass is not a physical piece of an object. It is a property of the object as a whole. Many forces which act on the pieces of the object can be treated as though they were acting directly on the center of mass.

As an example, gravity attracts two masses together. The gravity of the earth attracts every single atom in the ring in your example. We could take the time to sum them all up, but it would take a while. Instead, we can show that mathematically, the sum of all of those little tiny gravitational attractions between the atoms in the ring and the earth act as though they were one large force applied at the center of mass. In the case of the ring, there doesn't happen to be an atom at that center of mass, but it represents the effect of all the individual atoms and the forces on them, summed as a whole.


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