Angular velocity in the context of Rotate

In physics, the Coriolis force is a pseudo force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.

Newton's laws of motion describe the motion of an object in an inertial (non-accelerating) frame of reference. When Newton's laws are transformed to a rotating frame of reference, the Coriolis and centrifugal accelerations appear. When applied to objects with masses, the respective forces are proportional to their masses. The magnitude of the Coriolis force is proportional to the rotation rate, and the magnitude of the centrifugal force is proportional to the square of the rotation rate. The Coriolis force acts in a direction perpendicular to two quantities: the angular velocity of the rotating frame relative to the inertial frame and the velocity of the body relative to the rotating frame, and its magnitude is proportional to the object's speed in the rotating frame (more precisely, to the component of its velocity that is perpendicular to the axis of rotation). The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame. These additional forces are termed inertial forces, fictitious forces, or pseudo forces. By introducing these fictitious forces to a rotating frame of reference, Newton's laws of motion can be applied to the rotating system as though it were an inertial system; these forces are correction factors that are not required in a non-rotating system.

The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. The term Archimedean spiral is sometimes used to refer to the more general class of spirals of this type (see below), in contrast to Archimedes' spiral (the specific arithmetic spiral of Archimedes). It is the locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation$${\displaystyle r=b\cdot \theta }$$with real number b. Changing the parameter b controls the distance between loops.

From the above equation, it can thus be stated: position of the particle from point of start is proportional to angle θ as time elapses.

In Newtonian mechanics, a centrifugal force is a kind of fictitious force (or inertial force) that appears to act on all objects when viewed in a rotating frame of reference. It appears to be directed perpendicularly from the axis of rotation of the frame. The magnitude of the centrifugal force F on an object of mass m at the perpendicular distance ρ from the axis of a rotating frame of reference with angular velocity ω is ${\textstyle F=m\omega ^{2}\rho }$.

The concept of centrifugal force simplifies the analysis of rotating devices by adopting a co-rotating frame of reference, such as in centrifuges, centrifugal pumps, centrifugal governors, and centrifugal clutches, and in centrifugal railways, planetary orbits and banked curves. The same centrifugal effect observed on rotating devices can be analyzed in an inertial reference frame as a consequence of inertia and the physical forces without invoking a centrifugal force.

Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere. When the rays are lines of sight from an observer to two points in space, it is known as the apparent distance or apparent separation.

Angular distance appears in mathematics (in particular geometry and trigonometry) and all natural sciences (e.g., kinematics, astronomy, and geophysics). In the classical mechanics of rotating objects, it appears alongside angular velocity, angular acceleration, angular momentum, moment of inertia and torque.

Power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. Power is a scalar quantity.

The output power of a motor is the product of the torque that the motor generates and the angular velocity of its output shaft. Likewise, the power dissipated in an electrical element of a circuit is the product of the current flowing through the element and of the voltage across the element.

A fictitious force, also known as an inertial force or pseudo-force, is a force that appears to act on an object when its motion is described or experienced from a non-inertial frame of reference. Unlike real forces, which result from physical interactions between objects, fictitious forces occur due to the acceleration of the observer’s frame of reference rather than any actual force acting on a body. These forces are necessary for describing motion correctly within an accelerating frame, ensuring that Newton's second law of motion remains applicable.

Common examples of fictitious forces include the centrifugal force, which appears to push objects outward in a rotating system; the Coriolis force, which affects objects moving relative to the rotating frame, such as a wind parcel on Earth; and the Euler force, which arises when a rotating system changes its angular velocity (i.e., due to angular acceleration).

Greenwich Mean Time (GMT) is the local mean time at the Royal Observatory in Greenwich, London, counted from midnight. At different times in the past, it has been calculated in different ways, including being calculated from noon; as a consequence, it cannot be used to specify a particular time unless a context is given. The term "GMT" is also used as one of the names for the time zone UTC+00:00 and, in UK law, is the basis for civil time in the United Kingdom.

Because of Earth's uneven angular velocity in its elliptical orbit and its axial tilt, noon (12:00:00) GMT is rarely the exact moment the Sun crosses the Greenwich Meridian and reaches its highest point in the sky there. This event may occur up to 16 minutes before or after noon GMT, a discrepancy described by the equation of time. Noon GMT is the annual average (the arithmetic mean) moment of this event, which accounts for the word "mean" in "Greenwich Mean Time".

A fishing rod or fishing pole is a long, thin rod used by anglers to catch fish by manipulating a line ending in a hook (formerly known as an angle, hence the term "angling"). At its most basic form, a fishing rod is a straight rigid stick/pole with a line fastened to one end (as seen in traditional bamboo rod fishing such as Tenkara fishing); however, modern rods are usually more elastic and generally have the line stored in a reel mounted at the rod handle, which is hand-cranked and controls the line retrieval, as well as numerous line-restricting rings (also known as line guides) that distribute bending stress along the rod and help dampening down/prevent line whipping and entanglement. To better entice fish, baits or lures are dressed onto the hook attached to the line, and a bite indicator (e.g. a float) is typically used, some of which (e.g. quiver tip) might be incorporated as part of the rod itself.

Fishing rods act as an extended lever and allow the angler to amplify line movements while luring and pulling the fish. It also enhances casting distance by increasing the launch speed of the terminal tackles (the hook, bait/lure, and other accompanying attachments such as float and sinker/feeder), as a longer swing radius (compared to that of a human arm) corresponds to greater arc speed at the tip under the same angular velocity. The length of fishing rods usually vary between 0.6 m (2 ft) and 4.6 m (15 ft) depending on the style of angling, while the Guinness World Record is 22.45 m (73 ft 7.9 in).

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 gyroscope (from Ancient Greek γῦρος gŷros 'round' and σκοπέω skopéō 'to look') is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotation (spin axis) is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, due to the conservation of angular momentum.

Gyroscopes based on other operating principles also exist, such as the microchip-packaged MEMS gyroscopes found in electronic devices (sometimes called gyrometers), solid-state ring lasers, fibre optic gyroscopes, and the extremely sensitive quantum gyroscope.

Thrust vectoring, also known as thrust vector control (TVC), is the ability of an aircraft, rocket or other vehicle to manipulate the direction of the thrust from its engine(s) or motor(s) to control the attitude or angular velocity of the vehicle.

In rocketry and ballistic missiles that fly outside the atmosphere, aerodynamic control surfaces are ineffective, so thrust vectoring is the primary means of attitude control. Exhaust vanes and gimbaled engines were used in the 1930s by Robert Goddard.

In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under continuous rigid transformations such as rotations or translations, but which does not transform like a vector under certain discontinuous rigid transformations such as reflections. For example, the angular velocity of a rotating object is a pseudovector because, when the object is reflected in a mirror, the reflected image rotates in such a way so that its angular velocity "vector" is not the mirror image of the angular velocity "vector" of the original object; for true vectors (also known as polar vectors), the reflection "vector" and the original "vector" must be mirror images.

One example of a pseudovector is the normal to an oriented plane. An oriented plane can be defined by two non-parallel vectors, a and b, that span the plane. The vector a × b is a normal to the plane (there are two normals, one on each side – the right-hand rule will determine which), and is a pseudovector. This has consequences in computer graphics, where it has to be considered when transforming surface normals.In three dimensions, the curl of a polar vector field at a point and the cross product of two polar vectors are pseudovectors.

Stellar rotation is the angular motion of a star about its axis. The rate of rotation can be measured from the spectrum of the star, or by timing the movements of active features on the surface.

The rotation of a star produces an equatorial bulge due to centrifugal force. As stars are not solid bodies, they can also undergo differential rotation. Thus the equator of the star can rotate at a different angular velocity than the higher latitudes. These differences in the rate of rotation within a star may have a significant role in the generation of a stellar magnetic field.

In classical mechanics, the Euler force is the fictitious tangential forcethat appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axes. The Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration or transverse acceleration, is that part of the absolute acceleration that is caused by the variation in the angular velocity of the reference frame.

In physics, angular frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves).Angular frequency (or angular speed) is the magnitude of the pseudovector quantity angular velocity.

Angular frequency can be obtained by multiplying rotational frequency, ν (or ordinary frequency, f) by a full turn (2π radians): ω = 2π rad⋅ν.It can also be formulated as ω = dθ/dt, the instantaneous rate of change of the angular displacement, θ, with respect to time, t.