# Statics

## Summary

- Statics is the branch of mechanics dealing with forces acting on objects that are not accelerating.
- Equilibrium is a general concept that can refer to states of…
- static equilibrium, which includes…
- translational equilibrium (the equilibrium of forces)
- rotational equilibrium (the equilibrium of torques)

- dynamic equilibrium, which includes but is not limited to…
- thermodynamic equilibrium (the equilibrium of internal energy transfer)

- static equilibrium, which includes…
- An adjective before the noun is not needed when the type of equilibrium is known from context.
- This section of this book is about translational equilibrium only.
- Other forms of equilibrium will be dealt with in other sections of this book.

- An object is in translational equilibrium when…
- it is not accelerating
- the net force on it is zero.

- Tests for 2 forces in equilibrium
- Two forces are in equilibrium if they are
- equal (have equal magnitudes) and
- opposite (180° apart).

- Two forces are in equilibrium if they are
- Tests for 3 forces in equilibrium
- Resultant-equilibrant
- Select two forces and find their resultant.
- The remaining force is called an equilibrant if it is equal and opposite this resultant.

- Triangle of forces
- Three forces are in equilibrium if they can be arranged head-to-tail in any order to form a triangle.

- Resultant-equilibrant
- Tests for
*n*forces in equilibrium- Polygon of forces
- Three or more forces are in equilibrium if they can be arranged head-to-tail in any order to form a closed polygon.

- No net force
- Resolve all the forces acting on an object into components in some convenient coordinate system.
- Combine all the components along each axis.
- Add the components parallel to each axis.
- Then subtract the components anti-parallel to each axis.

- If the total along each axis is zero then the object is in equilibrium. For example…
- All the longitudinal forces cancel (forward-backward)
- All the lateral forces cancel (side to side).
- All the vertical forces cancel (up and down).

∑ *F*_{x}= 0⎫

⎪

⎬

⎪

⎭⇒ ∑ **F**= 0∑ *F*_{y}= 0∑ *F*_{z}= 0

- Balanced forces
- Resolve all the forces acting on an object into components in some convenient coordinate system.
- Combine the components along each axis in the positive and negative directions separately.
- Add just the components parallel to each axis.
- Add just the components anti-parallel to each axis.

- If the totals along each axis in opposite directions are equal, then the object is in equilibrium. For example…
- All the forward forces equal all the backward forces.
- All the leftward forces equal all the rightward forces.
- All the upward forces equal all the downward forces.

∑ *F*_{−x}= ∑*F*_{+x}⎫

⎪

⎬

⎪

⎭⇒ ∑ **F**= 0∑ *F*_{−y}= ∑*F*_{+y}∑ *F*_{−z}= ∑*F*_{+z}

- Polygon of forces