What is meant by term equilibrium ? State the conditions for the equilibrium of rigid bodies.

Explanation

A rigid body is said to be in equilibrium if both linear momentum and angular momentum of rigid body remains constant with time. (So, for equilibrium of a rigid body the linear acceleration of its centre of mass and also angular acceleration of the rigid body about any. axis should be zero.) The conditions of equilibrium for rigid body are as:
i) Translational Equilibrium:
The resultant of all external forces acting on the body must be zero.
i.e. `sumF_("ext") = 0`
or `sumF_x = 0 , sumF_y = 0 and sumF_z=0`
As `sumF_("ext") =0`
So `sumF_("ext")=Mveca_(c.m.)=M(dvecv_(cm))/(dt)=0`
As `M ne 0`
Therefore, `(dvecv_(cm))/(dt) = 0`, which means
`vecv_(cm)` = constant
It means, in translational equilibrium either body.is at rest or is in uniform motion.