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Centre of mass
the point at which the mass of an object can be thought to be concentrated
Suspended equilibrium
A state after when an object is released and comes to rest with its centre of mass below the point of suspension.
Freely suspended
If a suspended object returns to its equilibrium position after the turning force is taken away
Where is the centre of mass for a symmetrical object?
the intersection of the axis of symmetry
How to find the centre of mass?
Make a small hole in the object and hang it up so that it is free to swing without obstruction.
Hang a plumb line (a piece of string with a weight hanging from it) from the same suspension point. This lets you mark the vertical line directly below the suspension point.
Drill another hole at a different location within the object.
Again hang a plumb line to determine the vertical and mark it on.
The point at which the two marked lines cross is the centre of mass.