# Conditions for equilibrium

We learned in Sections 4.2 and 5.1 that a particle is in equilibrium—that is, the

particle does not accelerate—in an inertial frame of reference if the vector sum

of all the forces acting on the particle is zero, ΣFS= 0. For an extended body,

the equivalent statement is that the center of mass of the body has zero acceleration

if the vector sum of all external forces acting on the body is zero, as discussed in

Section 8.5. This is often called the first condition for equilibrium:

A second condition for an extended body to be in equilibrium is that the body

must have no tendency to rotate. A rigid body that, in an inertial frame, is not

rotating about a certain point has zero angular momentum about that point. If it

is not to start rotating about that point, the rate of change of angular momentum

must also be zero. From the discussion in Section 10.5, particularly Eq. (10.29),

this means that the sum of torques due to all the external forces acting on the

body must be zero. A rigid body in equilibrium can’t have any tendency to start

rotating about any point, so the sum of external torques must be zero about any

point. This is the second condition for equilibrium:

In this chapter we’ll apply the first and second conditions for equilibrium to situations

in which a rigid body is at rest (no translation or rotation). Such a body is said to be in static equilibrium (Fig. 11.1).

But the same conditions apply to a rigid body in uniform translational motion (without rotation),

such as an airplane in flight with constant speed, direction, and altitude. Such a body is in

equilibrium but is not static.

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