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The direction of vector rotation is counterclockwise if θ is positive (e.g. 90°), and clockwise if θ is negative (e.g. −90°) for ().Thus the clockwise rotation matrix is found as
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 .
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. A rotation is different from other types of motions: translations , which have no fixed points, and (hyperplane) reflections , each of them having an entire ( n − 1) -dimensional flat of ...
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").
When viewed at a position along the positive z-axis, the ¼ turn from the positive x-to the positive y-axis is counter-clockwise. For left-handed coordinates, the above description of the axes is the same, except using the left hand; and the ¼ turn is clockwise. Interchanging the labels of any two axes reverses the handedness.
A sphere rotating (spinning) about an axis. Rotation or rotational motion is the circular movement of an object around a central line, known as an axis of rotation.A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation.
This definition is independent of the object's direction of rotation about its axis. This implies that an object's direction of rotation, when viewed from above its north pole, may be either clockwise or counterclockwise. The direction of rotation exhibited by most objects in the solar system (including Sun and Earth) is counterclockwise. Venus ...
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. [3] [4] A chemical compound that causes dextrorotation is dextrorotatory or dextrorotary, while a compound that causes laevorotation is laevorotatory or laevorotary. [5]