The Physics
Hypertextbook
Opus in profectus

# 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)
• 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).
• 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.
• 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).
 ∑Fx = 0 ⎫⎪⎬⎪⎭ ⇒ ∑F = 0 ∑Fy = 0 ∑Fz = 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