Rotation around a fixed axis

Sphere rotating around one of its diameters
An example of rotation. Each part of the worm drive—both the worm and the worm gear—is rotating on its own axis.

Special case of rotational motion.

- Rotation around a fixed axis

294 related topics

Relevance

Centrifugal force

Inertial force that appears to act on all objects when viewed in a rotating frame of reference.

In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line. However, the observer (brown dot) who is standing in the rotating/non-inertial frame of reference (lower part of the picture) sees the object as following a curved path due to the Coriolis and centrifugal forces present in this frame.
The interface of two immiscible liquids rotating around a vertical axis is an upward-opening circular paraboloid.
When analysed in a rotating reference frame of the planet, centrifugal force causes rotating planets to assume the shape of an oblate spheroid.

It is directed away from an axis which is parallel to the axis of rotation and passing through the coordinate system's origin.

Angular velocity

In physics, angular velocity or rotational velocity ('''

The angular velocity of the particle at P with respect to the origin O is determined by the perpendicular component of the velocity vector v.
The orbital angular velocity vector encodes the time rate of change of angular position, as well as the instantaneous plane of angular displacement. In this case (counter-clockwise circular motion) the vector points up.
Schematic construction for addition of angular velocity vectors for rotating frames
Diagram showing Euler frame in green
Position of point P located in the rigid body (shown in blue). Ri is the position with respect to the lab frame, centered at O and ri is the position with respect to the rigid body frame, centered at . The origin of the rigid body frame is at vector position R from the lab frame.
Proving the independence of spin angular velocity from choice of origin

Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin.

Right-hand rule

Common mnemonic for understanding orientation of axes in three-dimensional space.

Finding the direction of the cross product by the right-hand rule
Conventional direction of the axis of a rotating body
Left-handed coordinates on the left, right-handed coordinates on the right.
Left- and right-handed screws
Prediction of direction of field (B), given that the current I flows in the direction of the thumb
Finding direction of magnetic field (B) for an electrical coil
Illustration of the right-hand rule on the ninth series of the Swiss 200-francs banknote.

In mathematics, a rotating body is commonly represented by a pseudovector along the axis of rotation.

Precession

Change in the orientation of the rotational axis of a rotating body.

Precession of a gyroscope
The response of a rotating system to an applied torque. When the device swivels, and some roll is added, the wheel tends to pitch.
Apsidal precession—the orbit rotates gradually over time.

In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself.

Nutation

Rotation, precession, and nutation in obliquity of a planet
Yearly changes in the location of the Tropic of Cancer near a highway in Mexico

Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism.

Rotation

A sphere rotating (spinning) about an axis
Rotation (angular displacement) of a planar figure around a point
Rotational Orbit v Spin
Relations between rotation axis, plane of orbit and axial tilt (for Earth).
Star trails caused by the Earth's rotation during the camera's long exposure time.
Euler rotations of the Earth. Intrinsic (green), Precession (blue) and Nutation (red)
The principal axes of rotation in space

Rotation is the circular movement of an object around an axis of rotation.

Rigid body

Solid body in which deformation is zero or so small it can be neglected.

The position of a rigid body is determined by the position of its center of mass and by its attitude (at least six parameters in total).

Two points of a rotating body will have the same instantaneous velocity only if they happen to lie on an axis parallel to the instantaneous axis of rotation.

Center of mass

Unique point where the weighted relative position of the distributed mass sums to zero.

This toy uses the principles of center of mass to keep balance when sitting on finger.
Diagram of an educational toy that balances on a point: the center of mass (C) settles below its support (P)
Plumb line method
Two bodies orbiting their barycenter (red cross)

Typically, a human's center of mass is detected with one of two methods: the reaction board method is a static analysis that involves the person lying down on that instrument, and use of their static equilibrium equation to find their center of mass; the segmentation method relies on a mathematical solution based on the physical principle that the summation of the torques of individual body sections, relative to a specified axis, must equal the torque of the whole system that constitutes the body, measured relative to the same axis.

Phonograph

Device for the mechanical and analogue recording and reproduction of sound.

Thomas Edison with his second phonograph, photographed by Levin Corbin Handy in Washington, April 1878
Edison Standard Phonograph, uses wax cylinders
Close up of the mechanism of an Edison Amberola, circa 1915
Early phonograph at Deaf Smith County Historical Museum in Hereford, Texas
Boy and toy record player, 1920s
222x222px
222x222px
Patent drawing for Edison's phonograph, May 18, 1880
Phonograph cabinet built with Edison cement, 1912. The clockwork portion of the phonograph is concealed in the base beneath the statue; the amplifying horn is the shell behind the human figure.
A 'G' (Graham Bell) model Graphophone being played back by a typist after its cylinder had recorded dictation.
A later-model Columbia Graphophone of 1901
A Victor V phonograph, circa 1907
A 1930s portable wind-up gramophone from EMI (His Master's Voice)
Philco all-transistor model TPA-1 phonograph, developed and produced in 1955
Philco all-transistor model TPA-1 phonograph – Radio and Television News magazine, issue October 1955
A Polish-made Unitra turntable atop an Electromureș (Unitra-Diora) receiver, circa 1979
Diagram of a turntable from a 1970 instruction manual
Adjustable counterweight; the dial below is the anti-skating adjustment.
Typical phonograph tonearm
Technics SL-Q6 linear tracking turntable
Typical magnetic cartridge
Stylus for jukebox using shellac 78 rpm records, 1940s
Cross-section diagram comparing two common types of stylus. Spherical (left), Elliptical (right). Note the difference in contact area of each type of needle marked in red. The spherical stylus makes less contact with the groove and generates less fidelity. The elliptical stylus allows for more groove contact area, which increases fidelity.
A phonograph for record preservation at Fonoteca Nacional (National Sound Archive of Mexico)

While the cylinder was rotated and slowly progressed along its axis, the airborne sound vibrated a diaphragm connected to a stylus that indented the foil into the cylinder's groove, thereby recording the vibrations as "hill-and-dale" variations of the depth of the indentation.

Polar motion

Motion of the Earth's rotational axis relative to its crust.

Polar motion in arc-seconds as function of time in days (0.1 arcsec ≈ 3 meters).
Figure 2. Rotation vector m of the annual component of polar motion as function of year. Numbers and tick marks indicate the beginning of each calendar month. The dash-dotted line is in the direction of the major axis. The line in the direction of the minor axis is the location of the excitation function vs. time of year. ( on the Earth's surface at the poles)

If the earth were perfectly symmetrical and rigid, M would remain aligned with its axis of symmetry, which would also be its axis of rotation.