Math 2.0

Mechanics of particles and systems Kinematics Concept

Angular velocity

Builds on VelocitySpecial orthogonal groupCross product

Summary

Angular velocity measures how fast and about which axis something turns. In three dimensions it is a vector along the axis of rotation, oriented by the right-hand rule. Its length is the rate of turning in radians per unit time. For a turning body or frame, the velocity of each point at position rr from a point of the axis is the cross product ω×r\omega \times r. It is the time derivative of a rotation, expressed through the Lie algebra of the rotation group.

Reading path

To understand this page from the ground up, read these 17 pages in order. The foundations come first.

Show the path as a graph
Cross product, concept, no evidence levelCross productconceptDerivative, concept, no evidence levelDerivativeconceptEuclidean vector, concept, no evidence levelEuclidean vectorconceptIdentity matrix, object, no evidence levelIdentity matrixobjectMatrix, definition, no evidence levelMatrixdefinitionVector space, definition, no evidence levelVector spacedefinitionVelocity, concept, no evidence levelVelocityconceptSquare matrix, definition, no evidence levelSquare matrixdefinitionTranspose, definition, no evidence levelTransposedefinitionLinear map, definition, no evidence levelLinear mapdefinitionOrthogonal matrix, definition, no evidence levelOrthogonal matrixdefinitionMultilinear map, definition, no evidence levelMultilinear mapdefinitionOrthogonal 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 velocityconcept
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 vector concept
  4. Identity matrix object
  5. Matrix definition
  6. Vector space definition
  7. Velocity concept
  8. Square matrix definition
  9. Transpose definition
  10. Linear map definition
  11. Orthogonal matrix definition
  12. Multilinear map definition
  13. Orthogonal group object
  14. Alternating multilinear map definition
  15. Determinant definition
  16. Special orthogonal group object
  17. Angular velocity concept

Where this leads

59 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Angular_velocity
About this page
Tag2FTZ7D8Z0F
URIm2://2FTZ7D8Z0F
Kindconcept
WritingW0 stub
MSC70B05, 70B10
UsesVelocity, Special orthogonal group, Cross product
Same as
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

Definitions

Used by