The First Condition for Equilibrium

The first condition necessary to achieve equilibrium is the one already mentioned: the net external force on the system must be zero. Expressed as an equation, this is simply

net F = 0 size 12{"net "F=0} {}

Note that if net F size 12{F} {}

is zero, then the net external force in any direction is zero. For example, the net external forces along the typical x- and y-axes are zero. This is written as

net Fx=0 andFy=0 size 12{"net "F rSub { size 8{y} } =0} {}

[link] and [link] illustrate situations where netF=0 size 12{"net"`F=0} {}

for both static equilibrium (motionless), and dynamic equilibrium (constant velocity).

In the figure, a stationary man is standing on the ground. His feet are at a distance apart. His hands are at his waist. The left side is labeled as net F is equal to zero. At the right side a free body diagram is shown with one point and two arrows, one vertically upward labeled as N and another vertically downward labeled as W, from the point.

A moving car is shown. Four normal vectors at each wheel are shown. At the rear wheel, a rightward arrow labeled as applied F is shown. Another arrow, which is labeled as f and points left, toward the front of the car, is also shown. A green vector at the top of the car shows the constant velocity vector. A free-body diagram is shown at the right with a point. From the point, the weight of the car is downward. Friction force vector f is toward left and applied force vector is toward right. Four normal vectors are shown upward above the point.

However, it is not sufficient for the net external force of a system to be zero for a system to be in equilibrium. Consider the two situations illustrated in [link] and [link] where forces are applied to an ice hockey stick lying flat on ice. The net external force is zero in both situations shown in the figure; but in one case, equilibrium is achieved, whereas in the other, it is not. In [link], the ice hockey stick remains motionless. But in [link], with the same forces applied in different places, the stick experiences accelerated rotation. Therefore, we know that the point at which a force is applied is another factor in determining whether or not equilibrium is achieved. This will be explored further in the next section.

A hockey stick is shown. At the middle point of the stick, two red colored force vectors are shown one pointing to the right and the other to the left. The line of action of the two forces is the same. The top of the figure is labeled as net force F is equal to zero. At the lower right side the free body diagram, a point with two horizontal vectors, each labeled F and directed away from the point, is shown.

A hockey stick is shown. The two force vectors acting on the hockey stick are shown, one pointing to the right and the other to the left. The lines of action of the two forces are different. Each vector is labeled as F. At the top and the bottom of the stick there are two circular arrows, showing the clockwise direction of the rotation. At the lower right side the free body diagram, a point with two horizontal vectors, each labeled F and directed away from the point, is shown.

PhET Explorations: Torque

Investigate how torque causes an object to rotate. Discover the relationships between angular acceleration, moment of inertia, angular momentum and torque.

[Torque](torque_en.jar)

Section Summary

Conceptual Questions

What can you say about the velocity of a moving body that is in dynamic equilibrium? Draw a sketch of such a body using clearly labeled arrows to represent all external forces on the body.

Under what conditions can a rotating body be in equilibrium? Give an example.

Glossary

static equilibrium
a state of equilibrium in which the net external force and torque acting on a system is zero
dynamic equilibrium
a state of equilibrium in which the net external force and torque on a system moving with constant velocity are zero
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