How things balance

A very useful concept in physics is Center of Gravity (AKA CM, Center of Mass - they are usually the same point).  

Recall the demo with the mass on a stick.  Same mass, held at a further distance from the "fulcrum", is harder to support.  It twists your wrist more - it requires a greater "torque".

So, what is torque?

Torque - a "rotating" force

T = F L

For an object to be "in equilibrium," not only must the forces be balanced, but the torques must also be balanced.

Consider a basic see-saw, initially balanced at the fulcrum:  See image below.

You can have two people of different weight balanced, if their distances are adjusted accordingly:  the heavier person is closer to the fulcrum.  

Mathematically, this requires that the torques be equal on both sides.

Consider two people, 100 lb and 200 lb.  The 100 lb person is 3 feet from the fulcrum.  How far from the fulcrum must the 200 lb person sit, to maintain equilibrium?

Torque on left = Torque on right

100 (3) = 200 (x)

x = 1.5 feet

NOTE:  The weights are NOT equal on both sides of the balance point.  But the torques ARE EQUAL.

We call the "balance point" the center of mass (or center of gravity).  

It is the point about which the object best rotates.

It is the weighted (by distance) average location of mass points on the object.

It does not HAVE to be physically on the object - think of a doughnut.

The principle is believed to originate with Archimedes (287 - 212 BC).  He is believed to have said, "Give me a place to stand on, and I will move the Earth."

FYI:  http://en.wikipedia.org/wiki/Archimedes