Math 2.0

Mechanics of particles and systems Definition

Statics

Builds on Mechanical equilibriumRigid bodyTorqueInertial frame of reference

Definition

Fix an inertial frame. A system of rigid bodies and particles is in static equilibrium if all its points are at rest in this frame at all times. Statics is the part of mechanics that determines the forces and torques in systems in static equilibrium. It also determines the configurations in which such equilibrium is possible. Its basic equations are the conditions of mechanical equilibrium for each body of the system. Let the forces FiF_i act on the body at the points pip_i, and let OO be any reference point. Then ∑iFi=0,∑i(pi−O)×Fi=0.\sum_i F_i = 0, \qquad \sum_i (p_i - O) \times F_i = 0.

Remarks

By Newton's second law, a body at rest has zero acceleration, so the forces on it balance; this is why the equilibrium conditions hold.

Example: a weightless plank on two supports at x=0x = 0 and x=4x = 4 carries a load of 600600 newtons at x=1x = 1. The support forces R0R_0 and R4R_4 satisfy R0+R4=600R_0 + R_4 = 600 and, taking torques about 00, 4R4=6004 R_4 = 600. So R4=150R_4 = 150 and R0=450R_0 = 450 newtons.

Non-example: a spinning wheel whose centre is fixed satisfies both equilibrium equations, yet its points are moving, so it is not in static equilibrium and lies outside statics. In the plane the equations give three scalar equations per body; a structure with more unknown support forces than equations is called statically indeterminate.

Reading path

To understand this page from the ground up, read these 8 pages in order. The foundations come first.

Show the path as a graph
Euclidean space, object, no evidence levelEuclidean spaceobjectMechanical equilibrium, concept, no evidence levelMechanical equilibriumconceptOrdinary differential equation, concept, no evidence levelOrdinary differential…conceptRigid body, concept, no evidence levelRigid bodyconceptTorque, concept, no evidence levelTorqueconceptClassical mechanics, concept, no evidence levelClassical mechanicsconceptInertial frame of reference, concept, no evidence levelInertial frame of ref…conceptStatics, definition, no evidence levelStaticsdefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Euclidean space object
  2. Mechanical equilibrium concept
  3. Ordinary differential equation concept
  4. Rigid body concept
  5. Torque concept
  6. Classical mechanics concept
  7. Inertial frame of reference concept
  8. Statics definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Statics
About this page
TagYQ7Q4Z3P6R
URIm2://YQ7Q4Z3P6R
Kinddefinition
WritingW0 stub
MSC70C20
DefinesStatics
UsesMechanical equilibrium, Rigid body, Torque, Inertial frame of reference
Changed3 November 2026

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • a source with a locator (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.