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In mathematics and physics, the plate trick, also known as Dirac's string trick (after Paul Dirac, who introduced and popularized it), [1] [2] the belt trick, or the Balinese cup trick (it appears in the Balinese candle dance), is any of several demonstrations of the idea that rotating an object with strings attached to it by 360 degrees does not return the system to its original state, while ...
The above definition is part of the ISQ, formalized in the international standard ISO 80000-3 (Space and time), [87] and adopted in the International System of Units (SI). [88] [89] Rotation count or number of revolutions is a quantity of dimension one, resulting from a ratio of angular displacement. It can be negative and also greater than 1 ...
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.
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).
[b] A spinor transforms linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation, [c] but unlike geometric vectors and tensors, a spinor transforms to its negative when the space rotates through 360° (see picture). It takes a rotation of 720° for a spinor to go back to its original state.
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]
A rotation of the vector through an angle θ in counterclockwise direction is given by the rotation matrix: = ( ), which can be viewed either as an active transformation or a passive transformation (where the above matrix will be inverted), as described below.
In particular, if a beam of spin-oriented spin- 1 / 2 particles is split, and just one of the beams is rotated about the axis of its direction of motion and then recombined with the original beam, different interference effects are observed depending on the angle of rotation. In the case of rotation by 360°, cancellation effects are ...