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In three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which always exists by virtue of the Euler's rotation theorem; the magnitude specifies the rotation in radians about that axis (using the right-hand rule to determine direction).
Change in angular displacement per unit time is called angular velocity with direction along the axis of rotation. The symbol for angular velocity is and the units are typically rad s −1. Angular speed is the magnitude of angular velocity.
In physics, angular velocity (symbol ω or , the lowercase Greek letter omega), also known as the angular frequency vector, [1] is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.
The time-rate of change of angular frequency is angular acceleration (rad/s 2), caused by torque. The ratio of torque τ to the angular acceleration α is given by the moment of inertia: =. The angular velocity vector (an axial vector) also describes the direction of the axis of rotation. Similarly, the torque is an axial vector.
When a direction is assigned to rotational speed, it is known as rotational velocity, a vector whose magnitude is the rotational speed. ( Angular speed and angular velocity are related to the rotational speed and velocity by a factor of 2 π , the number of radians turned in a full rotation.)
A yaw rotation is a movement around the yaw axis of a rigid body that changes the direction it is pointing, to the left or right of its direction of motion. The yaw rate or yaw velocity of a car, aircraft, projectile or other rigid body is the angular velocity of this rotation, or rate of change of the heading angle when the aircraft is ...
Angular velocity: the angular velocity ω is the rate at which the angular position θ changes with respect to time t: = The angular velocity is represented in Figure 1 by a vector Ω pointing along the axis of rotation with magnitude ω and sense determined by the direction of rotation as given by the right-hand rule.
The direction of the torque can be determined by using the right hand grip rule: ... If the torque and the angular displacement are in the same direction, ...