Define center of gravity.?

Question

I am looking to define "center of gravity" in relation to torque...i.e. torque arms, etc. Imagine a ruler on a pivot point, then how would I define its' center of gravity??

Answer 1

Center of gravity is based on geometry - it's the mass weighted-average of all the components. NASA has a good, simple explanation using a rocket as an example below:

Answer 2

the center of gravity i guess

Answer 3

Given set of particles of masses {m_i} and at vector positions {r_i}

r_cm = Sigma m_i * r_i/Sigma m_i