Given several compact objects of known mass and position, you can find the center of mass of the group in the following way:
or, in a more compact notation,
This method will work well as long as the size of each object is much smaller than the distance between the objects.
Example: given the 3 small objects in the picture below, with masses A = 5 kg, B = 2 kg, C = 4 kg, what is the location of their center of mass?
The Earth sits on the origin, at position x = 0. Where is the center of mass of the Earth/Moon system? Is it inside or outside the Earth? (Yes, you may need to look up some information ....)
Joe makes a circle of radius R out of sheet metal. He then cuts out a smaller circle of half the radius, R/2, so that it just touches the edge of the big circle.
Where is the center of mass of the remaining metal?
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