Axis of rotation in the context of "Spinning top"

A lathe (/leɪð/) is a machine tool that rotates a workpiece about an axis of rotation to perform various operations such as cutting, sanding, knurling, drilling, deformation, facing, threading and turning, with tools that are applied to the workpiece to create an object with symmetry about that axis.

Lathes are used in woodturning, metalworking, metal spinning, thermal spraying, reclamation, and glass-working. Lathes can be used to shape pottery, the best-known such design being the potter's wheel. Most suitably equipped metalworking lathes can be used to produce most solids of revolution, plane surfaces, and screw threads or helices. Ornamental lathes can produce more complex three-dimensional solids. The workpiece is usually held in place by either one or two centers, at least one of which can typically be moved horizontally to accommodate varying workpiece lengths. Other work-holding methods include clamping the work about the axis of rotation using a chuck or collet, or attaching it to a faceplate using clamps or dog clutch. Lathes equipped with special lathe milling fixtures can be used to complete milling operations.

In astronomy, diurnal motion (from Latin diurnus 'daily', from Latin diēs 'day') is the apparent motion of celestial objects (e.g. the Sun and stars) around Earth, or more precisely around the two celestial poles, over the course of one day. It is caused by Earth's rotation around its axis, so almost every star appears to follow a circular arc path, called the diurnal circle, often depicted in star trail photography.

The time for one complete rotation is 23 hours, 56 minutes, and 4.09 seconds – one sidereal day. The first experimental demonstration of this motion was conducted by Léon Foucault. Because Earth orbits the Sun once a year, the sidereal time at any given place and time will gain about four minutes against local civil time, every 24 hours, until, after a year has passed, one additional sidereal "day" has elapsed compared to the number of solar days that have gone by.

A geographical pole or geographic pole is either of the two points on Earth where its axis of rotation intersects its surface. The North Pole lies in the Arctic Ocean while the South Pole is in Antarctica. North and South poles are also defined for other planets or satellites in the Solar System, with a North pole being on the same side of the invariable plane as Earth's North pole.

Relative to Earth's surface, the geographic poles move by a few metres over periods of a few years. This is a combination of Chandler wobble, a free oscillation with a period of about 433 days; an annual motion responding to seasonal movements of air and water masses; and an irregular drift towards the 80th west meridian. As cartography and geodesy require exact and unchanging coordinates, the average or nominal locations of geographical poles are taken as fixed cartographic poles or geodetic poles, the points where the body's great circles of longitude intersect; in practice this is achieved by keeping latitude values of survey markers fixed and accounting for time variations in terms of Earth orientation parameters.

In astronomy, the rotation period or spin period of a celestial object (e.g., star, planet, moon, asteroid) has two definitions. The first one corresponds to the sidereal rotation period (or sidereal day), i.e., the time that the object takes to complete a full rotation around its axis relative to the background stars (inertial space). The other type of commonly used "rotation period" is the object's synodic rotation period (or solar day), which may differ, by a fraction of a rotation or more than one rotation, to accommodate the portion of the object's orbital period around a star or another body during one day.

The poles of astronomical bodies are determined based on their axis of rotation in relation to the celestial poles of the celestial sphere. Astronomical bodies include stars, planets, dwarf planets and small Solar System bodies such as comets and minor planets (e.g., asteroids), as well as natural satellites and minor-planet moons.

A pole star is a visible star that is approximately aligned with the axis of rotation of an astronomical body; that is, a star whose apparent position is close to one of the celestial poles. On Earth, a pole star would lie directly overhead when viewed from the North or the South Pole.

Currently, Earth's pole stars are Polaris (Alpha Ursae Minoris), a bright magnitude 2 star aligned approximately with its northern axis that serves as a pre-eminent star in celestial navigation, and a much dimmer magnitude 5.5 star on its southern axis, Polaris Australis (Sigma Octantis).

In physics and mechanics, torque is the rotational correspondent of linear force. It is also referred to as the moment of force, or simply the moment. The symbol for torque is typically ${\displaystyle {\boldsymbol {\tau }}}$, the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M. Just as a linear force is a push or a pull applied to a body, a torque can be thought of as a twist applied to an object with respect to a chosen point; for example, driving a screw uses torque to force it into an object, which is applied by the screwdriver rotating around its axis to the drives on the head.

Torque is generally referred to using different vocabulary depending on geographical location and field of study, with torque generally being associated with physics and moment being associated with engineering. This article follows the definition used in US physics in its usage of the word torque.

A hinge is a mechanical bearing that connects two solid objects, typically allowing only a limited angle of rotation between them. Two objects connected by an ideal hinge rotate relative to each other about a fixed axis of rotation, with all other translations or rotations prevented; thus a hinge has one degree of freedom. Hinges may be made of flexible material or moving components. In biology, many joints function as hinges, such as the elbow joint.

Hinges are frequently used on pivoting doors, but also are seen on folding ladders and many other flexible mechanisms such as automobile hoods (bonnets), and even large bridges.

Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space. This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will result.

This concept assumes that the rotation is also stable, such that no torque is required to keep it going. The kinematics and dynamics of rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body; they are entirely analogous to those of linear motion along a single fixed direction, which is not true for free rotation of a rigid body. The expressions for the kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational motion. For these reasons, rotation around a fixed axis is typically taught in introductory physics courses after students have mastered linear motion; the full generality of rotational motion is not usually taught in introductory physics classes.

Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.

For a satellite orbiting the Earth directly above the Equator, the plane of the satellite's orbit is the same as the Earth's equatorial plane, and the satellite's orbital inclination is 0°. The general case for a circular orbit is that it is tilted, spending half an orbit over the northern hemisphere and half over the southern. If the orbit swung between 20° north latitude and 20° south latitude, then its orbital inclination would be 20°.

In astronomy, axis mundi is the Latin term for the axis of Earth between the celestial poles. In a geocentric coordinate system, this is the axis of rotation of the celestial sphere. Consequently, in ancient Greco-Roman astronomy, the axis mundi is the axis of rotation of the planetary spheres within the classical geocentric model of the cosmos.

In 20th-century comparative mythology, the term axis mundi – also called the cosmic axis, world axis, world pillar, center of the world, or world tree – has been greatly extended to refer to any mythological concept representing "the connection between Heaven and Earth" or the "higher and lower realms". Mircea Eliade introduced the concept in the 1950s. Axis mundi closely relates to the mythological concept of the omphalos (navel) of the world or cosmos.Items presented as examples of the axis mundi by comparative mythologists include plants (notably a tree but also other types of plants such as a vine or stalk), a mountain, a column of smoke or fire, or a product of human manufacture (such as a staff, a tower, a ladder, a staircase, a maypole, a cross, a steeple, a rope, a totem pole, a pillar, a spire). Its proximity to heaven may carry implications that are chiefly religious (pagoda, Temple Mount, minaret, church) or secular (obelisk, lighthouse, rocket, skyscraper). The image appears in religious and secular contexts. The axis mundi symbol may be found in cultures utilizing shamanic practices or animist belief systems, in major world religions, and in technologically advanced "urban centers". In Mircea Eliade's opinion: "Every Microcosm, every inhabited region, has a Centre; that is to say, a place that is sacred above all."

A lunar day is the time it takes for Earth's Moon to complete on its axis one synodic rotation, meaning with respect to the Sun. The synodic period is about 29.53 Earth days, which is about 2.2 days longer than its sidereal period.

Informally, a lunar day and a lunar night are each approximately 14 Earth days. The formal lunar day is therefore the time of a full lunar day-night cycle.

An orbital pole is either point at the ends of the orbital normal, an imaginary line segment that runs through a focus of an orbit (of a revolving body like a planet, moon or satellite) and is perpendicular (or normal) to the orbital plane. Projected onto the celestial sphere, orbital poles are similar in concept to celestial poles, but are based on the body's orbit instead of its equator.

The north orbital pole of a revolving body is defined by the right-hand rule. If the fingers of the right hand are curved along the direction of orbital motion, with the thumb extended and oriented to be parallel to the orbital axis, then the direction the thumb points is defined to be the orbital north.

Astronomical nutation is a phenomenon which causes the orientation of the axis of rotation of a spinning astronomical object to vary over time. It is caused by the gravitational forces of other nearby bodies acting upon the spinning object. Although they are caused by the same effect operating over different timescales, astronomers usually make a distinction between precession, which is a steady long-term change in the axis of rotation, and nutation, which is the combined effect of similar shorter-term variations.

An example of precession and nutation is the variation over time of the orientation of the axis of rotation of the Earth. This is important because the most commonly used frame of reference for measurement of the positions of astronomical objects is the Earth's equator — the so-called equatorial coordinate system. The effect of precession and nutation causes this frame of reference itself to change over time, relative to an arbitrary fixed frame.

A ball bearing is a type of rolling-element bearing that uses balls to maintain the separation between the bearing races.

The purpose of a ball bearing is to reduce rotational friction and support radial and axial loads. It achieves this by using at least two races to contain the balls and transmit the loads through the balls. In most applications, one race is stationary and the other is attached to the rotating assembly (e.g., a hub or shaft). As one of the bearing races rotates it causes the balls to rotate as well. Because the balls are rolling, they have a much lower coefficient of friction than if two flat surfaces were sliding against each other.

In physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity. Following the two types of angular velocity, spin angular velocity and orbital angular velocity, the respective types of angular acceleration are: spin angular acceleration, involving a rigid body about an axis of rotation intersecting the body's centroid; and orbital angular acceleration, involving a point particle and an external axis.

Angular acceleration has physical dimensions of angle per time squared, with the SI unit radian per second squared (rad⋅s). In two dimensions, angular acceleration is a pseudoscalar whose sign is taken to be positive if the angular speed increases counterclockwise or decreases clockwise, and is taken to be negative if the angular speed increases clockwise or decreases counterclockwise. In three dimensions, angular acceleration is a pseudovector.

A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints).The volume bounded by the surface created by this revolution is the solid of revolution.

Examples of surfaces of revolution generated by a straight line are cylindrical and conical surfaces depending on whether or not the line is parallel to the axis. A circle that is rotated around any diameter generates a sphere of which it is then a great circle, and if the circle is rotated around an axis that does not intersect the interior of a circle, then it generates a torus which does not intersect itself (a ring torus).