Static is the part of mechanics that studies the conditions for a body to be at rest (**static equilibrium**). It is applied in architecture and civil engineering to do structural calculations.

For a body to be in **static equilibrium**, two conditions must be met:

The first condition implies that the **acceleration of the center of mass of the system is null**, so it has no translational motion.

The second condition implies that the **angular acceleration of the system is null**, so it has no rotational motion. It must be fulfilled regardless of the point that is used to calculate the torques of the forces.

Therefore, Statics is a particular case of application of the rotational motion.

When you try to solve problems of Physics in general and Statics in particular, it is important to **follow a certain order**. Try to be systematic when you solve these problems, and you will see how it gives good results. It is worth spending a bit of time on the analysis of a problem before starting to solve it.

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When solving a Statics problem, follow these steps:

- Read carefully the problem statement.
- Draw a picture of the physical situation described in the problem.
- Write in your notebook the givens in the problem statement.
- Identify the elements that make up the system that should be in
**static equilibrium**: if it is a single body or if on the contrary you must take into account several objects. This step is important because it will allow you to distinguish the**internal and external forces**that act on the system. - Draw the
**external forces**that act on the system. - Remember that the forces are physical interactions. Therefore, if a system is supported on another system, a normal force will act on it; if it is close to the surface of the Earth, the weight will act on it, and so on with the rest of the interactions that the system experiences.
- In this link you can see how the forces exerted by the different types of support are represented.
- Add a Cartesian coordinate system on the drawing,
**indicating which is the positive direction of each of the axes**. you should also indicate which point you are going to use as an origin to calculate the torque of the external forces acting on the system. - Write the
**first condition of a static equilibrium in a vectorial form**, including in the vectorial sum the different external forces you have identified. - Project the resulting equation on the Cartesian axes. Take into account the sign of the different projections.
- Calculate the torques of the different external forces with respect to the point you have chosen as origin.
- Write the
**second condition of a static equilibrium in a vectorial form**. - Project the resulting equation on the Cartesian axes. Take into account the sign of the different projections.
- Solve the system of equations that you have obtained after projecting on the axes the two conditions of a static equilibrium. In this way you will be able to determine magniudes asked for in the problem.
- Do not forget to
**include the units**in your results. - Review the problem and check that the results you have obtained make sense.

On the following pages you will find solved problems of Statics**. Try to do them before looking at the solution**.