Rotation
Rotation is the movement of an object in a circular motion. A two-
dimensional object rotates around a center of rotation. A three-dimensional object rotates around a line called an axis. If the axis of rotation is within the body, the body is said to rotate upon itself, or spin— which implies relative speed and perhaps free-movement with
angular momentum. A circular motion about an external point is called an orbit or more properly orbital revolution.
Encyclopedia
Rotation is the movement of an object in a circular motion. A two-
dimensional object rotates around a
center of rotation. A three-dimensional object rotates around a line called an
axis. If the axis of rotation is within the body, the body is said to rotate upon itself, or
spin— which implies relative speed and perhaps free-movement with
angular momentum. A circular motion about an external point is called an
orbit or more properly
orbital revolution.Mathematics
Mathematically, a rotation is a rigid body movement which keeps a point fixed; unlike a
translation. This definition is applicable both for rotations in a plane and in space . It turns out that a rotation in the three-dimensional space keeps fixed not just a single point, but rather an entire line; that is to say, any rotation in the three-dimensional space is a rotation around an axis. This is a consequence of Euler's rotation theorem.
Any rigid body movement is in fact either a rotation, or a translation, or a combination of the two.
If one does a rotation around a point , followed by another rotation around the same point , the total result is yet another rotation. The reverse of a rotation is also a rotation. It follows that the rotations around a point or axis form a group. If however one performs rotation around a point followed by rotation around another point , the overall movement may not be a rotation anymore; it can for example be a translation.
Principal axes of rotation
Rotations around the
x,
y and
z axes are called
principal rotations. Rotation around any axis can be performed by taking a rotation around the
x axis, followed by a rotation around the
y axis, and followed by a rotation around the
z axis. That is to say, any spatial rotation can be decomposed into a combination of principal rotations.
In
flight dynamics, the principal rotations are known as
pitch,
roll and
yaw. This terminology is also used in computer graphics.
See also: curl,
cyclic permutation,
Euler angles, rigid body, rotation around a fixed axis, rotation group, rotation matrix, isometry.
Astronomy
In
astronomy, rotation is a commonly observed phenomenon.
Stars,
planets and similar bodies all spin around on their axes . The rotation rate of planets in the solar system was first measured by tracking visual features.
This rotation induces a
centrifugal acceleration which slightly counteracts the effect of gravity the closer one is to the
equator. One effect is that an object weighs slightly less at the equator. Another is that the Earth is slightly deformed into an
oblate spheroid.
Another consequence of the rotation of a planet is the phenomenon of
precession. Like a
gyroscope, the overall effect is a slight "wobble" in the movement of the axis of a planet. Currently the tilt of the
Earth's axis to its orbital plane is 66.5 degrees, but this angle changes slowly .
Revolution
Moons also revolve about their planet, planets revolve about their star ; and stars slowly revolve about their
galaxial center. The motion of the components of
galaxies is complex, but it usually includes a rotation component.
The Moon makes one complete rotation during one complete revolution around the Earth so that the same side of the Moon always faces the Earth .
Retrograde rotation
Most
planets in our
solar system, including
Earth, spin in the same direction as they orbit the
Sun. The exceptions are
Venus and
Uranus. Uranus rotates nearly on its side relative to its orbit. Current speculation is that Uranus started off with a typical prograde orientation and was knocked on its side by a large impact early in its history. Venus may be thought of as rotating slowly backwards . The
dwarf planet Pluto is anomalous in this and other ways.
Physics
The speed of rotation is given by the
angular frequency or
frequency , or period . The time-rate of change of angular frequency is angular acceleration , This change is caused by
torque. The ratio of the two is given by the moment of inertia.
The
angular velocity vector also describes the direction of the axis of rotation. Similarly the torque is a vector.
According to the
right-hand rule, the direction away from the observer is associated with clockwise rotation and the direction towards the observer with counterclockwise rotation, like a
screw.
Amusement rides
Many
amusement rides provide rotation. A
Ferris wheel and
observation wheel have a horizontal central axis, and parallel axes for each gondola, where the rotation is opposite, by gravity or mechanically. As a result at any time the orientation of the gondola is upright , just translated. The tip of the translation vector describes a circle. A
carousel provides rotation about a vertical axis. Many rides provide a combination of rotations about several axes. In
Chair-O-Planes the rotation about the vertical axis is provided mechanically, while the rotation about the horizontal axis is due to the
centrifugal force. In roller coaster inversions the rotation about the horizontal axis is one or more full cycles, where the centrifugal force keeps people in their seats.
Sports
Rotation, usually called
spin, plays a role in many sports.
Topspin and
backspin in
tennis.
English,
follow and
draw in
billiards and pool.
Curve balls in baseball and spin bowling in cricket.
See also
External links
- at cut-the-knot
- at cut-the-knot
- at Math is Fun
