Math 2.0

Mechanics of particles and systems Definition

Coriolis force

Builds on Fictitious forceRotating reference frameAngular velocityVelocity

Definition

Let a rotating reference frame have angular velocity Ω(t)\Omega(t), expressed in the axes of the frame. Let a particle of mass m>0m > 0 have velocity vv relative to the rotating frame, also in those axes. The Coriolis force on the particle is FCor=−2m Ω×v.F_{\mathrm{Cor}} = -2m\, \Omega \times v. It is one of the terms of the fictitious force in the rotating frame.

Remarks

Example: on the Earth the angular speed is ∣Ω∣≈7.29×10−5\abs\Omega \approx 7.29 \times 10^{-5} rad/s; take a body at the North Pole moving horizontally with speed 1010 m/s. There Ω\Omega is vertical, so the Coriolis force is horizontal, perpendicular to vv and to the right of the motion, and its size per unit mass is 2∣Ω∣⋅10≈1.46×10−32 \abs\Omega \cdot 10 \approx 1.46 \times 10^{-3} m/s2^2. Non-example: the centrifugal force −m Ω×(Ω×X)-m\,\Omega \times (\Omega \times X) is a fictitious force but not the Coriolis force. It depends on the position XX and not on the velocity, and it acts even on a body at rest in the frame, where the Coriolis force is 00. Since FCor⋅v=0F_{\mathrm{Cor}} \cdot v = 0, the Coriolis force does no work. A body moving parallel to Ω\Omega feels no Coriolis force.

Reading path

To understand this page from the ground up, read these 26 pages in order. The foundations come first.

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Cross product, concept, no evidence levelCross productconceptDerivative, concept, no evidence levelDerivativeconceptEuclidean space, object, no evidence levelEuclidean spaceobjectEuclidean vector, concept, no evidence levelEuclidean vectorconceptIdentity matrix, object, no evidence levelIdentity matrixobjectMatrix, definition, no evidence levelMatrixdefinitionOrdinary differential equation, concept, no evidence levelOrdinary differential…conceptVector space, definition, no evidence levelVector spacedefinitionVelocity, concept, no evidence levelVelocityconceptClassical mechanics, concept, no evidence levelClassical mechanicsconceptSquare matrix, definition, no evidence levelSquare matrixdefinitionTranspose, definition, no evidence levelTransposedefinitionLinear map, definition, no evidence levelLinear mapdefinitionMomentum, concept, no evidence levelMomentumconceptInertial frame of reference, concept, no evidence levelInertial frame of ref…conceptOrthogonal matrix, definition, no evidence levelOrthogonal matrixdefinitionMultilinear map, definition, no evidence levelMultilinear mapdefinitionNewton's laws of motion, statement, no evidence levelNewton's laws of moti…statementOrthogonal group, object, no evidence levelOrthogonal groupobjectAlternating multilinear map, definition, no evidence levelAlternating multiline…definitionDeterminant, definition, no evidence levelDeterminantdefinitionSpecial orthogonal group, object, no evidence levelSpecial orthogonal gr…objectAngular velocity, concept, no evidence levelAngular velocityconceptRotating reference frame, concept, no evidence levelRotating reference fr…conceptFictitious force, concept, no evidence levelFictitious forceconceptCoriolis force, definition, no evidence levelCoriolis forcedefinition
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. Cross product concept
  2. Derivative concept
  3. Euclidean space object
  4. Euclidean vector concept
  5. Identity matrix object
  6. Matrix definition
  7. Ordinary differential equation concept
  8. Vector space definition
  9. Velocity concept
  10. Classical mechanics concept
  11. Square matrix definition
  12. Transpose definition
  13. Linear map definition
  14. Momentum concept
  15. Inertial frame of reference concept
  16. Orthogonal matrix definition
  17. Multilinear map definition
  18. Newton's laws of motion statement
  19. Orthogonal group object
  20. Alternating multilinear map definition
  21. Determinant definition
  22. Special orthogonal group object
  23. Angular velocity concept
  24. Rotating reference frame concept
  25. Fictitious force concept
  26. Coriolis force definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Coriolis_force
About this page
TagPQPECN7X33
URIm2://PQPECN7X33
Kinddefinition
WritingW0 stub
MSC70B05, 70A05
DefinesCoriolis force
UsesFictitious force, Rotating reference frame, Angular velocity, Velocity
Changed3 November 2026

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