Angular velocity

Gives the angular velocity vector as the time derivative of angular displacement, pointing along the axis of rotation. It is used to describe how fast a body rotates and in which direction.

\boldsymbol{\omega} = \frac{\mathrm{d} \varphi}{\mathrm{d} t} \boldsymbol{u}

What the symbols mean

angular velocity vector (rad/s)
angular displacement (rad)
time (s)
unit vector along the axis of rotation

About this formula

  • FieldPhysics
  • TopicRotational kinematics
  • LevelHigh school
  • Also calledangular velocity vector, rate of change of angular displacement, rotational velocity, angular velocity formula, omega vector rotation axis, angular speed times unit vector
  • SourceWikidata Q161635

Write it in Obsidian

MathLive is a free visual math editor for Obsidian. Run Find a formula, type “angular velocity”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.

Related formulas