1.
Rotation
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A rotation is a circular movement of an object around a center of rotation. A three-dimensional object always rotates around a line called a rotation axis. If the axis passes through the center of mass, the body is said to rotate upon itself. A rotation about a point, e. g. the Earth about the Sun, is called a revolution or orbital revolution. The axis is called a pole, mathematically, a rotation is a rigid body movement which, unlike a translation, keeps a point fixed. This definition applies to rotations within both two and three dimensions All rigid body movements are rotations, translations, or combinations of the two, a rotation is simply a progressive radial orientation to a common point. That common point lies within the axis of that motion, the axis is 90 degrees perpendicular to the plane of the motion. If the axis of the rotation lies external of the body in question then the body is said to orbit, there is no fundamental difference between a “rotation” and an “orbit” and or spin. The key distinction is simply where the axis of the rotation lies and this distinction can be demonstrated for both “rigid” and “non rigid” bodies. If a rotation around a point or axis is followed by a rotation around the same point/axis. The reverse of a rotation is also a rotation, thus, the rotations around a point/axis form a group. However, a rotation around a point or axis and a rotation around a different point/axis may result in something other than a 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 that is to say, any spatial rotation can be decomposed into a combination of principal rotations. In flight dynamics, the rotations are known as yaw, pitch. This terminology is used in computer graphics. In astronomy, rotation is an 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. Stellar rotation is measured through Doppler shift or by tracking active surface features and this rotation induces a centrifugal acceleration in the reference frame of the Earth which slightly counteracts the effect of gravity the closer one is to the equator

2.
Absolute rotation
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In physics, the concept of absolute rotation—rotation independent of any external reference—is a topic of debate about relativity, cosmology, and the nature of physical laws. For the concept of rotation to be scientifically meaningful, it must be measurable. In other words, can an observer distinguish between the rotation of an object and their own rotation. Newton suggested two experiments to resolve this problem, one is the effects of centrifugal force upon the shape of the surface of water rotating in a bucket. The second is the effect of force upon the tension in a string joining two spheres rotating about their center of mass. A related third example, given by Albert Einstein in the development of relativity, is a rotating elastic sphere. Like a rotating planet bulging at the equator, the sphere deforms into a squashed spheroid depending on its rotation, in general relativity no external causes are invoked. The rotation is relative to the local geodesics, and since the local geodesics eventually channel information from the distant stars, there appears to be absolute rotation relative to these stars. In theoretical physics, particularly in discussions of theories, Machs principle is the name given by Einstein to a hypothesis often credited to the physicist. The idea is that the motion of a rotating reference frame is determined by the large-scale distribution of matter in the universe. Machs principle says that there is a law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force, the principle is often stated in vague ways, like mass out there influences inertia here. Because rotating water has a surface, if the surface you see is concave. Centrifugal force is needed to explain the concavity of the water in a frame of reference because the water appears stationary in this frame. Thus, observers looking at the water need the centrifugal force to explain why the water surface is concave. If you need a force to explain what you see. Newtons conclusion was that rotation is absolute, other thinkers suggest that pure logic implies only relative rotation makes sense. Newton also proposed another experiment to measure rate of rotation

3.
Ambigram
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An ambigram is a word, art form or other symbolic representation whose elements retain meaning when viewed or interpreted from a different direction, perspective, or orientation. The meaning of the ambigram may either change, or remain the same, Douglas R. Hofstadter describes an ambigram as a calligraphic design that manages to squeeze two different readings into the selfsame set of curves. Different ambigram artists may create completely different ambigrams from the word or words. The earliest known non-natural ambigram dates to 1893 by artist Peter Newell, the last page in his book Topsys & Turvys contains the phrase THE END, which, when inverted, reads PUZZLE. In Topsys & Turvys Number 2, Newell ended with a variation on the ambigram in which THE END changes into PUZZLE2, from June to September,1908, the British monthly The Strand published a series of ambigrams by different people in its Curiosities column. Of particular interest is the fact all four of the people submitting ambigrams believed them to be a rare property of particular words. In 1969, Raymond Loewy designed the rotational NEW MAN ambigram logo, the mirror ambigram DeLorean Motor Company logo was first used in 1975. John Langdon and Scott Kim also each believed that they had invented ambigrams in the 1970s, Langdon and Kim are probably the two artists who have been most responsible for the popularization of ambigrams. John Langdon produced the first mirror image logo Starship in 1975, Robert Petrick, who designed the invertible Angel logo in 1976, was also an early influence on ambigrams. The earliest known published reference to the term ambigram was by Hofstadter, the original 1979 edition of Hofstadters Gödel, Escher, Bach featured two 3-D ambigrams on the cover. Langdon also produced the ambigram that was used for versions of the books cover. Brown used the name Robert Langdon for the hero in his novels as an homage to John Langdon, in music, the Grateful Dead have used ambigrams several times, including on their albums Aoxomoxoa and American Beauty. In the first series of the British show Trick or Treat and these cards can read either Trick or Treat. The Transformers movie series have logos that are a robot face whether viewed right side up or upside down, there are two such logos, one for an Autobot, and one for a Decepticon. In 2015 iSmarts logo on one of its travel chargers went viral because upside-down it read +Jews. The company noted that. we learned a lesson of what not to do when creating a logo. ”Ambigrams are exercises in graphic design that play with optical illusions, symmetry. Some ambigrams feature a relationship between their form and their content, ambigrams usually fall into one of several categories, 3-Dimensional A design where an object is presented that will appear to read several letters or words when viewed from different angles. Such designs can be generated using constructive solid geometry, chain A design where a word are interlinked, forming a repeating chain

4.
Angular momentum
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In physics, angular momentum is the rotational analog of linear momentum. It is an important quantity in physics because it is a conserved quantity – the angular momentum of a system remains constant unless acted on by an external torque. The definition of momentum for a point particle is a pseudovector r×p. This definition can be applied to each point in continua like solids or fluids, unlike momentum, angular momentum does depend on where the origin is chosen, since the particles position is measured from it. The angular momentum of an object can also be connected to the angular velocity ω of the object via the moment of inertia I. However, while ω always points in the direction of the rotation axis, Angular momentum is additive, the total angular momentum of a system is the vector sum of the angular momenta. For continua or fields one uses integration, torque can be defined as the rate of change of angular momentum, analogous to force. Applications include the gyrocompass, control moment gyroscope, inertial systems, reaction wheels, flying discs or Frisbees. In general, conservation does limit the motion of a system. In quantum mechanics, angular momentum is an operator with quantized eigenvalues, Angular momentum is subject to the Heisenberg uncertainty principle, meaning only one component can be measured with definite precision, the other two cannot. Also, the spin of elementary particles does not correspond to literal spinning motion, Angular momentum is a vector quantity that represents the product of a bodys rotational inertia and rotational velocity about a particular axis. Angular momentum can be considered an analog of linear momentum. Thus, where momentum is proportional to mass m and linear speed v, p = m v, angular momentum is proportional to moment of inertia I. Unlike mass, which only on amount of matter, moment of inertia is also dependent on the position of the axis of rotation. Unlike linear speed, which occurs in a line, angular speed occurs about a center of rotation. Therefore, strictly speaking, L should be referred to as the angular momentum relative to that center and this simple analysis can also apply to non-circular motion if only the component of the motion which is perpendicular to the radius vector is considered. In that case, L = r m v ⊥, where v ⊥ = v sin θ is the component of the motion. It is this definition, × to which the moment of momentum refers

5.
Rotating black hole
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A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry, there are four known, exact, black hole solutions to the Einstein field equations, which describe gravity in general relativity. Two of those rotate, the Kerr and Kerr–Newman black holes and these numbers represent the conserved attributes of an object which can be determined from a distance by examining its electromagnetic and gravitational fields. All other variations in the hole will either escape to infinity or be swallowed up by the black hole. This is because anything happening inside the black hole horizon cannot affect events outside of it, as most stars rotate it is expected that most black holes in nature are rotating black holes. In late 2006, astronomers reported estimates of the rates of black holes in the The Astrophysical Journal. A black hole in the Milky Way, GRS 1915+105, may rotate 1,150 times per second, the formation of a rotating black hole by a collapsar is thought to be observed as the emission of gamma ray bursts. A rotating black hole can produce large amounts of energy at the expense of its rotational energy and this happens through the Penrose process in the black holes ergosphere, an area just outside its event horizon. A rotating black hole is a solution of Einsteins field equation, there are two known exact solutions, the Kerr metric and the Kerr–Newman metric, which are believed to be representative of all rotating black hole solutions, in the exterior region. Kerr black holes as wormholes BKL singularity – solution representing interior geometry of black holes formed by gravitational collapse, melia, Fulvio, The Galactic Supermassive Black Hole, Princeton U Press,2007 Macvey, John W

6.
Centrifugal force
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In Newtonian mechanics, the centrifugal force is an inertial force directed away from the axis of rotation that appears to act on all objects when viewed in a rotating reference frame. When they are analyzed in a coordinate system. The term has also been used for the force that is a reaction to a centripetal force. The centrifugal force is an outward force apparent in a reference frame. All measurements of position and velocity must be relative to some frame of reference. An inertial frame of reference is one that is not accelerating, the use of an inertial frame of reference, which will be the case for all elementary calculations, is often not explicitly stated but may generally be assumed unless stated otherwise. In terms of a frame of reference, the centrifugal force does not exist. All calculations can be performed using only Newtons laws of motion, in its current usage the term centrifugal force has no meaning in an inertial frame. In an inertial frame, an object that has no acting on it travels in a straight line. When measurements are made with respect to a reference frame, however. If it is desired to apply Newtons laws in the frame, it is necessary to introduce new, fictitious. Consider a stone being whirled round on a string, in a horizontal plane, the only real force acting on the stone in the horizontal plane is the tension in the string. There are no forces acting on the stone so there is a net force on the stone in the horizontal plane. In an inertial frame of reference, were it not for this net force acting on the stone, in order to keep the stone moving in a circular path, this force, known as the centripetal force, must be continuously applied to the stone. As soon as it is removed the stone moves in a straight line, in this inertial frame, the concept of centrifugal force is not required as all motion can be properly described using only real forces and Newtons laws of motion. In a frame of reference rotating with the stone around the axis as the stone. However, the tension in the string is still acting on the stone, if Newtons laws were applied in their usual form, the stone would accelerate in the direction of the net applied force, towards the axis of rotation, which it does not do. With this new the net force on the stone is zero, with the addition of this extra inertial or fictitious force Newtons laws can be applied in the rotating frame as if it were an inertial frame

7.
Centripetal force
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A centripetal force is a force that makes a body follow a curved path. Its direction is orthogonal to the motion of the body. Isaac Newton described it as a force by which bodies are drawn or impelled, or in any way tend, in Newtonian mechanics, gravity provides the centripetal force responsible for astronomical orbits. One common example involving centripetal force is the case in which a body moves with uniform speed along a circular path, the centripetal force is directed at right angles to the motion and also along the radius towards the centre of the circular path. The mathematical description was derived in 1659 by the Dutch physicist Christiaan Huygens, the direction of the force is toward the center of the circle in which the object is moving, or the osculating circle. The speed in the formula is squared, so twice the speed needs four times the force, the inverse relationship with the radius of curvature shows that half the radial distance requires twice the force. Expressed using the orbital period T for one revolution of the circle, the rope example is an example involving a pull force. The centripetal force can also be supplied as a push force, newtons idea of a centripetal force corresponds to what is nowadays referred to as a central force. Another example of centripetal force arises in the helix that is traced out when a particle moves in a uniform magnetic field in the absence of other external forces. In this case, the force is the centripetal force that acts towards the helix axis. Below are three examples of increasing complexity, with derivations of the formulas governing velocity and acceleration, uniform circular motion refers to the case of constant rate of rotation. Here are two approaches to describing this case, assume uniform circular motion, which requires three things. The object moves only on a circle, the radius of the circle r does not change in time. The object moves with constant angular velocity ω around the circle, therefore, θ = ω t where t is time. Now find the velocity v and acceleration a of the motion by taking derivatives of position with respect to time, consequently, a = − ω2 r. negative shows that the acceleration is pointed towards the center of the circle, hence it is called centripetal. While objects naturally follow a path, this centripetal acceleration describes the circular motion path caused by a centripetal force. The image at right shows the relationships for uniform circular motion. In this subsection, dθ/dt is assumed constant, independent of time, consequently, d r d t = lim Δ t →0 r − r Δ t = d ℓ d t

8.
Circular motion
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In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, the rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body, since the objects velocity vector is constantly changing direction, the moving object is undergoing acceleration by a centripetal force in the direction of the center of rotation. Without this acceleration, the object would move in a straight line, in physics, uniform circular motion describes the motion of a body traversing a circular path at constant speed. Since the body describes circular motion, its distance from the axis of rotation remains constant at all times, though the bodys speed is constant, its velocity is not constant, velocity, a vector quantity, depends on both the bodys speed and its direction of travel. This changing velocity indicates the presence of an acceleration, this acceleration is of constant magnitude. This acceleration is, in turn, produced by a force which is also constant in magnitude. For motion in a circle of radius r, the circumference of the circle is C = 2π r, the axis of rotation is shown as a vector ω perpendicular to the plane of the orbit and with a magnitude ω = dθ / dt. The direction of ω is chosen using the right-hand rule, likewise, the acceleration is given by a = ω × v = ω ×, which is a vector perpendicular to both ω and v of magnitude ω |v| = ω2 r and directed exactly opposite to r. In the simplest case the speed, mass and radius are constant, consider a body of one kilogram, moving in a circle of radius one metre, with an angular velocity of one radian per second. The speed is one metre per second, the inward acceleration is one metre per square second, v2/r. It is subject to a force of one kilogram metre per square second. The momentum of the body is one kg·m·s−1, the moment of inertia is one kg·m2. The angular momentum is one kg·m2·s−1, the kinetic energy is 1/2 joule. The circumference of the orbit is 2π metres, the period of the motion is 2π seconds per turn. It is convenient to introduce the unit vector orthogonal to u ^ R as well and it is customary to orient u ^ θ to point in the direction of travel along the orbit. The velocity is the derivative of the displacement, v → = d d t r → = d R d t u ^ R + R d u ^ R d t. Because the radius of the circle is constant, the component of the velocity is zero