Equilibrium of a rigid body, moments, and center of gravity

Equilibrium Conditions

• For an object to be in equilibrium, the net force and net torque acting on it must be equal to zero.

Center of Gravity (CG)

• The center of gravity (CG) of an object is the point where the entire weight of the object is considered to be concentrated.

For a symmetric object, the CG is at its geometric center.

• The CG of a system of particles is the point where the total torque due to the weights of the particles is zero.

Methods for finding the CG

• For symmetric objects: the CG can be determined by inspection.

• For objects with simple shapes: the CG can be calculated using formulas.

• For irregular objects: the CG can be determined by the principle of moments.

Stability

• A body is in stable equilibrium if, when slightly disturbed from its equilibrium position, it tends to return to that position.

• A body is in unstable equilibrium if, when slightly disturbed from its equilibrium position, it tends to move away from that position.

• The stability of a body depends on the position of its CG.

An object is most stable when its CG is lowest.