An object is in equilibrium when the vector sum of all external forces acting on it is zero. According to Newton's Second Law, this means the object has no acceleration. If the object is at rest, it is in static equilibrium. If it is moving with constant velocity, it is in dynamic equilibrium. Since forces are vector quantities, equilibrium requires that the net force be zero along every coordinate axis. For motion in two dimensions, this means:

Consider Figure 60.1, which shows a person standing still. The upward normal force from the ground exactly balances the downward gravitational force (weight), so the net force is zero. Because the person remains at rest with no acceleration, they are in static equilibrium.

Now consider Figure 60.2. A car moving at constant velocity has balanced horizontal and vertical forces. The horizontal applied force is balanced by air resistance (a form of friction), and the vertical weight is balanced by the normal forces from the road. This is an example of dynamic equilibrium: the object moves but does not accelerate.

It’s important to note that having zero net force does not necessarily mean there is no motion. It simply means there is no change in motion (no acceleration). However, for a system to be truly in equilibrium, force balance alone is not sufficient. The location where a force is applied also matters, especially when considering rotational effects. Take a look at Figure 60.3 and Figure 60.4. In both cases, two equal and opposite forces act on a hockey stick. In Figure 60.3, the forces act along the same line of action, so the stick stays still. This is true equilibrium. But in Figure 60.4, the same forces act at different locations, producing a torque that causes the stick to rotate. Even though [latex]\text{net}\,\vec{F} = 0[/latex], the system is not in equilibrium because it experiences angular acceleration. We’ll return to this in the next section.

Interactive Exploration: Torque

Torque is the rotational equivalent of force. Just as a force can cause an object to accelerate in a straight line, a torque can cause an object to rotate about an axis. In this simulation, you'll investigate how the magnitude and direction of a force, the distance from the pivot point, and the object's moment of inertia influence rotational motion. Experiment by applying forces at different locations and in different directions. Observe how changing the point of application or the object's mass distribution affects the resulting rotation. As you explore, think about how these principles apply to everyday situations such as opening a door, using a wrench, riding a bicycle, or how muscles rotate bones around joints.