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In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .
The examples in this article apply to active rotations of vectors counterclockwise in a right-handed coordinate system (y counterclockwise from x) by pre-multiplication (R on the left). If any one of these is changed (such as rotating axes instead of vectors, a passive transformation ), then the inverse of the example matrix should be used ...
It can describe, for example, the motion of a rigid body around a fixed point. Rotation can have a sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude.
In the case of a plane simple closed curve (that is, a curve in the plane whose starting point is also the end point and which has no other self-intersections), the curve is said to be positively oriented or counterclockwise oriented, if one always has the curve interior to the left (and consequently, the curve exterior to the right), when ...
Dextrorotation and laevorotation (also spelled levorotation) [1] [2] in chemistry and physics are the optical rotation of plane-polarized light.From the point of view of the observer, dextrorotation refers to clockwise or right-handed rotation, and laevorotation refers to counterclockwise or left-handed rotation.
Kinematics insists that a force (pushing to the right of the instantaneous direction of travel for a counter-clockwise rotation) must be present to cause this curvature, so the rotating observer is forced to invoke a combination of centrifugal and Coriolis forces to provide the net force required to cause the curved trajectory. [citation needed]
For example, the daily rotation of the Earth is clockwise when viewed from above the South Pole, and counterclockwise when viewed from above the North Pole (considering "above a point" to be defined as "farther away from the center of earth and on the same ray"). The shadow of a horizontal sundial in the Northern Hemisphere rotates clockwise
For example, if the object first circles the origin four times counterclockwise, and then circles the origin once clockwise, then the total winding number of the curve is three. Using this scheme, a curve that does not travel around the origin at all has winding number zero, while a curve that travels clockwise around the origin has negative ...