Conditions of Equilibrium

A rigid body does not undergo any deformation under the influence of external forces.

Consider a merry-go-round subjected to an external force F at a perpendicular radial distance r, which results in the moment of a force about point O.

If multiple forces act on the merry-go-round, the equilibrium condition is obtained when the sum of all external forces acting on it is zero.

The other condition of equilibrium states that the sum of all moments about point O must equal zero.

When the moment is measured at point A, it can be expressed as the sum of the moment at point O and the cross product of perpendicular distance and the applied force.

These conditions ensure that the body does not undergo any translational or rotational motion in static equilibrium.

Only external forces are considered here since the internal forces within the rigid body have the same magnitude and act in opposite directions, canceling each other due to Newton's third law of motion.