A rigid object's motion is divided into position, momentum, and angular momentum. So, the 'axis of rotation' is the unit vector which is the object's angular momentum vector divided by the angular momentum magnitude (and is undefined when there's no angular momentum)..
What does rotation axis mean?
: the straight line through all fixed points of a rotating rigid body around which all other points of the body move in circles..
What is rotational symmetry in crystallography?
Rotational symmetries can be considered in a similar fashion. From one point in empty space, the view is the same regardless of which direction one looks. There is continuous rotational symmetry—namely, the symmetry of a perfect sphere. In the crystal shown in Figure .
A, however,…
What is the axis of rotation of a molecule?
This is also called an n-fold rotational axis and abbreviated Cn. Examples are the C2 axis in water and the C3 axis in ammonia. A molecule can have more than one symmetry axis; the one with the highest n is called the principal axis, and by convention is aligned with the z-axis in a Cartesian coordinate system..
What is the proper rotation axis?
Proper Rotation and Proper Axis (Cn) A "proper" rotation is just a simple rotation operation about an axis. The symbol for any proper rotation or proper axis is C(360/n), where n is the degree of rotation. Thus, a 180\xb0 rotation is a C2 rotation around a C2 axis, and a 120\xb0 rotation is a C3 rotation about a C3 axis..
What is the rotation axis?
: the straight line through all fixed points of a rotating rigid body around which all other points of the body move in circles..
A rotoinversion axis combines rotation about an axis of rotation with inversion. Rotoinversion axes are symbolized as 1, 2, 3, 4, and 6, where 1 is equivalent to a centre of symmetry (or inversion), 2 is equivalent to a mirror plane, and 3 is equivalent to…
In crystals, the symmetry axes (rotation axes) can only be two-fold (2), three-fold (3), four-fold (4) or six-fold (6), depending on the number of times (order of rotation) that a motif can be repeated by a rotation operation, being transformed into a new state indistinguishable from its starting state.
A rotation axis is an imaginary line through a crystal around which it may be rotated and repeat itself in appearance one, two, three, four, or six times during a complete rotation. (For example, a sixfold rotation occurs when the crystal repeats itself each 60°—that is,…
How do you find the direction of a fourfold rotation axis?
The direction of rotation axis u: The application of equation (1
2 2
14) with the matrix yields the direction u = of the fourfold rotation axis
Sense of rotation: The negative sense of rotation follows from det ( Z) = −1, where the matrix (here, is taken as a vector non-parallel to u )
What is a rotation axis?
This line is called the rotation axis
The degree of rotation about this axis is described by its rotation angle
Because of the periodicity of crystals, the rotation angles of crystallographic rotations are restricted to , where N = 2, 3, 4 or 6 and k is an integer which is relative prime to N
What is the rotation angle of a crystal?
Because of the periodicity of crystals, the rotation angles of crystallographic rotations are restricted to , where N = 2, 3, 4 or 6 and k is an integer which is relative prime to N
A rotation of rotation angle is of order N and is called an N -fold rotation
A rotation preserves the handedness of any chiral object
A rotation axis is an imaginary line through a crystal around which it may be rotated and repeat itself in appearance one, two, three, four, or six times during a complete rotation. (For example, a sixfold rotation occurs when the crystal repeats itself each 60°—that is,…
Crystallography rotation axis
Rotation of the plane of linearly polarized light as it travels through a chiral material
Optical rotation, also known as polarization rotation or circular birefringence, is the rotation of the orientation of the plane of polarization about the optical axis of linearly polarized light as it travels through certain materials. Circular birefringence and circular dichroism are the manifestations of optical activity. Optical activity occurs only in chiral materials, those lacking microscopic mirror symmetry. Unlike other sources of birefringence which alter a beam's state of polarization, optical activity can be observed in fluids. This can include gases or solutions of chiral molecules such as sugars, molecules with helical secondary structure such as some proteins, and also chiral liquid crystals. It can also be observed in chiral solids such as certain crystals with a rotation between adjacent crystal planes or metamaterials.
