How things balance

FYI - exams are not yet graded.  Sorry!

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.  There may be a single torque on each side of a lever, or there may be multiple torques on each side.  Actually, there may be an infinite number of torques on either side.  Furthermore, there don't have to just be 2 sides - if this is a 3-dimensional (real) body, it can have an infinite number of "lever arms".  Consider a frisbee - it is round, but it still balances about a single point.  What is this special point called?  See below.


Center of Mass

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 average weighted 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










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