Chapter 11 - Angular velocity

Abstract

Angular velocity is defined as the angle that an object rotates per unit time. In the International System of Units (SI) the angular velocity is measured in rad/s. Angular velocity is a property of rigid bodies and therefore is the same regardless of the point of the rigid body under analysis. Unlike linear velocity, angular velocity, being the same at any point of the rigid body, cannot be formulated as the time derivative of a vector. The character of vector is acquired by the angular velocity when certain conventions of vector algebra are used. For this reason, in the three-dimensional case the angular velocity vector is designated as an axial vector or pseudo vector which is parallel to the axis of rotation. The effect of angular velocity on a rigid body is such that while certain points of the body acquire maximum velocities other points of the same body may remain at rest. The relationship between points at rest and points in motion allows an immediate visualization of the kinematic behavior at the velocity level of a mechanism, as used in the graphical method of velocity analysis. The rotation of a rigid body is part of Chasles' theorem which allows to deduce the instantaneous axis of rotation as that axis of the rigid body in which the points have the same velocity. The angular velocity vector between two rigid bodies allows a systematic and elegant formulation of the time derivative of arbitrary vectors using various reference frames. This is a key issue in the analysis of acceleration of rotating systems, as is the case with the Coriolis acceleration.