![]() In two dimensions, the angular velocity ω is given by Therefore, the rotation is completely produced by the perpendicular motion around the origin, and the angular velocity is completely determined by this component. On the other hand, if there is no cross-radial component, then the particle moves along a straight line from the origin.Ī radial motion produces no change in the direction of the particle relative to the origin, so, for the purpose of finding the angular velocity, the radial component can be ignored. ![]() If there is no radial component, then the particle moves in a circle. As shown in the diagram (with angles ɸ and θ in radians), if a line is drawn from the origin (O) to the particle (P), then the velocity ( v) of the particle has a component along the radius (radial component, v ‖) and a component perpendicular to the radius (cross-radial component, v ⊥). The angular velocity of a particle is measured around or relative to a point, called the origin. The direction of the angular velocity pseudovector will be along the axis of rotation in this case (counter-clockwise rotation) the vector points up. The angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs.
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