angular velocity
, where a dot denotes differentiation with respect to time.
At a more advanced level, the angular velocity ω of the particle P is the vector defined by ω = θ˙ k, where i and j are unit vectors in the directions of the positive x- and y-axes, and k = i × j. If r and v are the position vector and velocity of P, then
where er = i cos θ + j sin θ and eθ =−i sinθ + j cos θ (see circular motion). By using the fact that k = er × eθ, it follows that the velocity v is given by v = ω × r.
Consider a rigid body rotating about a fixed axis, and take coordinate axes so that the z-axis is along the fixed axis. Let (r0, θ) be the polar coordinates of some point of the rigid body, not on the axis, lying in the plane z =0. Then the angular velocity ω of the rigid body is defined by 
.
In general, for a rigid body that is rotating, such as a top spinning about a fixed point, the rigid body possesses an angular velocity ω whose magnitude and direction depend on time, though the formula v = ω × r still applies.
- circular measure
- circular motion
- circulation
- circumcentre
- circumference
- circumscribe
- cis
- class
- class boundaries
- class equation
- classical mechanics
- Classification Theorem for Surfaces
- class interval
- class mark
- cleartext
- clock arithmetic
- clockwise
- clopen set
- closed
- closed
- closed disc
- closed-form
- closed interval
- closed set
- closed surface