# 9: Statics and Torque

How can we guarantee that a body is in equilibrium and what can we learn from systems that are in equilibrium? There are actually two conditions that must be satisfied to achieve equilibrium. These conditions are the topics of the first two sections of this chapter.

- 9.0: Prelude to Statics and Torque
- Statics is the study of forces in equilibrium, a large group of situations that makes up a special case of Newton’s second law. We have already considered a few such situations; in this chapter, we cover the topic more thoroughly, including consideration of such possible effects as the rotation and deformation of an object by the forces acting on it.

- 9.1: 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.

- 9.2: The Second Condition for Equilibrium
- The second condition necessary to achieve equilibrium involves avoiding accelerated rotation (maintaining a constant angular velocity. A rotating body or system can be in equilibrium if its rate of rotation is constant and remains unchanged by the forces acting on it. To understand what factors affect rotation, let us think about what happens when you open an ordinary door by rotating it on its hinges.

- 9.3: Stability
- There are three types of equilibrium: stable, unstable, and neutral. A system is in stable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in a direction opposite to the direction of the displacement. A system is in unstable equilibrium if, when displaced, it experiences a net force or torque in the same direction as the displacement from equilibrium. A neutral equilibrium is if its equilibrium is independent of displacements from its original position.

- 9.4: Applications of Statics, Including Problem-Solving Strategies
- Statics can be applied to a variety of situations, ranging from raising a drawbridge to bad posture and back strain. We begin with a discussion of problem-solving strategies specifically used for statics. Since statics is a special case of Newton’s laws, both the general problem-solving strategies and the special strategies for Newton’s laws, discussed in Problem-Solving Strategies, still apply.

- 9.5: Simple Machines
- Simple machines are devices that can be used to multiply or augment a force that we apply – often at the expense of a distance through which we apply the force. Levers, gears, pulleys, wedges, and screws are some examples of machines. Energy is still conserved for these devices because a machine cannot do more work than the energy put into it. Machines can reduce the input force that is needed to perform the job. The ratio of output to input force magnitudes is called its mechanical advantage.

- 9.6: Forces and Torques in Muscles and Joints
- Muscles, bones, and joints are some of the most interesting applications of statics. There are some surprises. Muscles, for example, exert far greater forces than we might think. Figure shows a forearm holding a book and a schematic diagram of an analogous lever system. The schematic is a good approximation for the forearm, which looks more complicated than it is, and we can get some insight into the way typical muscle systems function by analyzing it.

*Thumbnails: Relationship between force (F), torque(τ), momentum (p), and angular momentum (L) vectors in a rotating system. (r) is the radius. Image used with permission (Public domain; Yawe).*

### Contributors

Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).