angular velocity

angular velocity (plural angular velocities)

1. (mathematics, physics) The angle turned, per unit time, by a body rotating about an axis; the rate of rotation through an angle.
   • 1963, Richard Feynman, The Feynman Lectures on Physics (1963) Ch. 18 Rotation in Two Dimensions, 18–2 Rotation of a rigid body.

     First, we have the angle θ which defines how far the body has gone around; this replaces the distance s, which defines how far it has gone along. In the same manner, we have a velocity of turning, ω=dθ/dt, which tells us how much the angle changes in a second, just as v=ds/dt describes how fast a thing moves, or how far it moves in a second. If the angle is measured in radians, then the angular velocity ω will be so and so many radians per second. The greater the angular velocity, the faster the object is turning, the faster the angle changes.

   • Wikipedia: Differential

     A differential is a device, usually, but not necessarily, employing gears, which is connected to the outside world by three shafts, through which it transmits torque and rotation. The gears or other components make the three shafts rotate in such a way that ${\displaystyle a=pb+qc}$, where a, b, and c are the angular velocities of the three shafts, and p and q are constants. [...] In automobiles and other wheeled vehicles, a differential allows the driving road wheels to rotate at different speeds. This is necessary when the vehicle turns, making the wheel that is traveling around the outside of the turning curve roll farther and faster than the other. The engine is connected to the shaft rotating at angular velocity a. The driving wheels are connected to the other two shafts, and p and q are equal.^WP

• angle
• angular acceleration
• radian