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432 CHAPTER 14 Statics and Elasticity

(a) stable equilibrium (b) unstable equilibrium (c) neutral equilibrium
string
Chair is suspended
from a point above
center of mass.

Chair is supported
at center of mass.

Chair is supported
from a point below
center of mass.

FIGURE 14.3 A body (a) in stable
equilibrium; (b) in unstable equilibrium; A body suspended from a point above its center of mass, as in Fig. 14.3a, is in stable
(c) in neutral equilibrium. equilibrium (see also Section 8.2). If we turn this body through some angle, so the
center of mass is no longer vertically below the point of support, the force of gravity
and the supporting force will produce a torque that tends to return the body to the
equilibrium position. In contrast, if this body is supported by a single force applied at a
point below the center of mass, as in Fig. 14.3b, the body is in unstable equilibrium. If we
turn the body ever so slightly, the force of gravity and the supporting force will produce
a torque that tends to turn the body farther away from the equilibrium position—the
body tends to topple over. Finally, a body supported by a single force at its center of mass,
as in Fig. 14.3c, is in neutral equilibrium. If we turn such a body, it remains in equi-
librium in its new position, and exhibits no tendency to return to its original position
or to turn farther away.
Similar stability criteria apply to the translational motion of a body moving on a
surface. A body is in stable equilibrium if it resists small disturbances and tends to
return to its original position when the disturbance ceases. A car resting at the bottom
of a dip in the road is an example of this kind of equilibrium; if we displace the car
forward and then let go, the car rolls back to its original position. A body is in unsta-
ble equilibrium if it tends to move away from its original position when disturbed. A
car resting on the top of a hill is an example of this second kind of equilibrium. If we
displace the car forward, it continues to roll down the hill. A car resting on a flat street
is in neutral equilibrium with respect to translational displacements. If we displace the
car along the street, it merely remains at the new position, without any tendency to
return to its original position or to move away from it (see Fig. 14.4).
The first four examples of the next section involve stable or neutral equilibrium; the
next two examples involve unstable equilibrium. Engineers take great care to avoid
unstable equilibrium in the design of structures and machinery, since an unstable con-
figuration will collapse or come apart at the slightest provocation.

(a) stable equilibrium (b) unstable equilibrium (c) neutral equilibrium
A displaced car A displaced car
moves back to remains at the
equilibrium. new position.

A displaced car
moves farther away
from equilibrium.

FIGURE 14.4 Stationary automobile in (a) stable, (b) unstable, and (c) neutral equilibrium.