12.2:
Static Equilibrium – II
Consider a rod rotating freely in a vertical plane. If two equal weights are attached to each side of the rod, a static equilibrium can be established when both the net force and the net torque are balanced in the system.
In a free body diagram, the gravitational force on each weight acts downward, while a normal force equal to the sum of the weights attached acts upward at the pivot point, thus balancing the forces in the system.
If the weights are at an equal distance from the axis of rotation, the torques acting at these points are equal in magnitude but act in the opposite direction, making the net torque zero. Thus, a static equilibrium is established.
If one weight is moved closer to the axis of rotation, the torque due to this weight reduces. As a result, there is a net torque that rotates the rod.
Although the net force is balanced in the system, it is not in static equilibrium as the second condition is violated.
12.2:
Static Equilibrium – II
Static equilibrium is a special case in mechanics that is very important in everyday life. It occurs when the net force and the net torque on an object or system are both zero. This means that both the linear and angular accelerations are zero. Thus, the object is at rest, or its center of mass is moving at a constant velocity. However, this does not mean that no forces are acting on the object within the system. In fact, there are very few scenarios on Earth in which no forces are acting upon any given object. If a person walks across a bridge, for example, they exert a downward force on the bridge proportional to their mass, and the bridge exerts an equal and opposite upward force on the person. In some cases, the bridge may flex in response to the downward force of the person, and in extreme cases, when the forces are great enough, the bridge may become seriously deformed or may even fracture.
The application of static equilibrium can be seen in bridges, towers, and other complex systems. For instance, all bridges are under some amount of stress, from both their own weight and the weight of the loads moving across. Suspension bridges, like the Golden Gate bridge, are a complex system of objects under very heavy forces and in equilibrium. The cables that hold the bridge up are elastic, and their elasticity was considered when the structural engineers designed it. Similarly, skyscrapers have a complex system of steel beams under tremendous forces, which altogether compose a rigid system in static equilibrium. Elasticity plays a role in the materials used to construct buildings, as they need to be able to withstand a certain amount of flexing, especially in areas where earthquakes are prevalent. Furthermore, the cranes used to construct these buildings are also in equilibrium, with a complex system of cables and pulleys to lift and lower the construction materials.
This text is adapted from Openstax, University of Physics Volume 1, Section 12.1: Conditions for Static Equilibrium.