Center of Mass / Center of Gravity

The Center of Gravity (CG) of an object can be thought of as several things:

- the point about which an object best rotates

- the point on which an object best balances

- the point where all "Torques" are balanced*

- a fictitious point, not even necessarily ON the object (consider a donut)

* Torque - the produce of weight and distance; W d

It is easy to visualize the CG concept with a simple see-saw:

W1 W2

------------o--------------

d1 d2

Weights are W and distances are d.

Two people (W1 and W2) are balanced on a see-saw; however, for balance/equilibrium, they don't have to have the same weight. The product of their weight and distance (from the fulcrum) must be equal. That is, the torque on the left (W1 d1) must equal the torque on the right (W2 d2).

So, the CG of the see-saw above is the point where the torques are balanced - NOT the weights. In other words, the weight on both sides are NOT equal; the torques are.

For something to be stable, the CG must be supported - either by a base below or above the CG. Consider the demonstrations from class.

- spoon / fork

- balancing guy

- Ernest the balancing bear

- the balancing meter stick lever (like a see-saw)

- balancing a meter stick on your finger

- the CG of a man vs. a woman