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A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
The inclination of the moon's orbit is shown relative to the Ecliptic Plane. The Solar System traces out a sinusoidal path in its orbit around the galactic center. Using Galactic North as the initial frame of reference, the Earth and Sun rotate counterclockwise, and the Earth revolves in a counterclockwise direction around the Sun.
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.
In the passive transformation (right), point P stays fixed, while the coordinate system rotates counterclockwise by an angle θ about its origin. The coordinates of P ′ after the active transformation relative to the original coordinate system are the same as the coordinates of P relative to the rotated coordinate system.
The counterclockwise or anticlockwise direction Two-dimensional rotation can occur in two possible directions or senses of rotation. Clockwise motion (abbreviated CW ) proceeds in the same direction as a clock 's hands relative to the observer: from the top to the right, then down and then to the left, and back up to the top.
The Capital Beltway around Washington, D.C., is signed by all four compass directions at various points, but is consistently signed with inner–outer labeling.. In nations where automobiles drive on the right side of a road, traffic traveling in a clockwise direction around a loop will always be in the "inner" lane(s) (assuming that there is no lane crossing).
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
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]