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Rotation, sometimes called rotation pool, 15-ball rotation, or 61, is a pool game, played with a pocketed billiards table, cue ball, and triangular rack of fifteen billiard balls, in which the lowest-numbered object ball on the table must be always struck by the cue ball first, to attempt to pocket numbered balls for points.
In mathematics, a rotating body is commonly represented by a pseudovector along the axis of rotation. The length of the vector gives the speed of rotation and the direction of the axis gives the direction of rotation according to the right-hand rule: right fingers curled in the direction of rotation and the right thumb pointing in the positive ...
The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of its ...
"Chicago" often refers to a variation of rotation pool in which the balls are initially placed in positions against the rails of the table. [2] [3]Another variation of Chicago is played in a similar fashion to nine-ball and rotation, where balls must be played in order starting with the 1 ball.
Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.
If the ball has a rough surface, the fluid flowing past it will make it rotate. The rotation axis (oriented according to the right hand rule) points in the direction of the curl of the field at the center of the ball, and the angular speed of the rotation is half the magnitude of the curl at this point. [9]
The rotation occurs in the sense prescribed by the right-hand rule. The rotation axis is sometimes called the Euler axis . The axis–angle representation is predicated on Euler's rotation theorem , which dictates that any rotation or sequence of rotations of a rigid body in a three-dimensional space is equivalent to a pure rotation about a ...
In three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which always exists by virtue of the Euler's rotation theorem; the magnitude specifies the rotation in radians about that axis (using the right-hand rule to determine direction).