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51 relations: Angular acceleration, Angular displacement, Angular frequency, Angular momentum, Angular velocity, Antisymmetric tensor, Areal velocity, Brady Haran, Davenport chained rotations, Dot product, Dual space, Euclidean vector, Euler angles, Euler's rotation theorem, Evgeny Lifshitz, Exterior algebra, Frame (linear algebra), Geosynchronous orbit, Gimbal, Hodge star operator, Instant centre of rotation, International System of Units, Isometry, Killing vector field, Leonhard Euler, Lie algebra, Lie group, Linear form, Musical isomorphism, Omega, Orthogonal group, Orthogonal transformation, Parity (physics), Physics, Polar coordinate system, Pseudoscalar, Pseudovector, Radian, Radian per second, Right-hand rule, Rigid body, Rigid body dynamics, Rotation, Rotation group SO(3), Rotation matrix, Skew-symmetric matrix, Three-dimensional space, University of Nottingham, Vector field, Versor, ..., Vorticity. Expand index (1 more) »
Angular acceleration
Angular acceleration is the rate of change of angular velocity.
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Angular displacement
Angular displacement of a body is the angle in radians (degrees, revolutions) through which a point revolves around a centre or line has been rotated in a specified sense about a specified axis.
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Angular frequency
In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate.
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Angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum.
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Angular velocity
In physics, the angular velocity of a particle is the rate at which it rotates around a chosen center point: that is, the time rate of change of its angular displacement relative to the origin.
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Antisymmetric tensor
In mathematics and theoretical physics, a tensor is antisymmetric on (or with respect to) an index subset if it alternates sign (+/−) when any two indices of the subset are interchanged.
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Areal velocity
In classical mechanics, areal velocity (also called sector velocity or sectorial velocity) is the rate at which area is swept out by a particle as it moves along a curve.
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Brady Haran
Brady John Haran (born 18 June 1976) is an Australian-born British independent filmmaker and video journalist who is known for his educational videos and documentary films produced for BBC News and his YouTube channels, the most notable being Periodic Videos and Numberphile.
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Davenport chained rotations
In physics and engineering, Davenport chained rotations are three chained intrinsic rotations about body-fixed specific axes.
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Dual space
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
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Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
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Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.
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Euler's rotation theorem
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point.
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Evgeny Lifshitz
Evgeny Mikhailovich Lifshitz (Евге́ний Миха́йлович Ли́фшиц; February 21, 1915, Kharkov, Russian Empire – October 29, 1985, Moscow, Russian SFSR) was a leading Soviet physicist and the brother of physicist Ilya Mikhailovich Lifshitz.
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Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
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Frame (linear algebra)
In linear algebra, a frame of an inner product space is a generalization of a basis of a vector space to sets that may be linearly dependent.
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Geosynchronous orbit
A geosynchronous orbit (sometimes abbreviated GSO) is an orbit around Earth of a satellite with an orbital period that matches Earth's rotation on its axis, which takes one sidereal day (23 hours, 56 minutes, and 4 seconds).
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Gimbal
A gimbal is a pivoted support that allows the rotation of an object about a single axis.
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Hodge star operator
In mathematics, the Hodge isomorphism or Hodge star operator is an important linear map introduced in general by W. V. D. Hodge.
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Instant centre of rotation
The instant center of rotation, also called instantaneous velocity center, or also instantaneous center or instant center, is the point fixed to a body undergoing planar movement that has zero velocity at a particular instant of time.
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International System of Units
The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement.
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Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
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Killing vector field
In mathematics, a Killing vector field (often just Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Lie algebra
In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.
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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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Linear form
In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalars.
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Musical isomorphism
In mathematics, the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle TM and the cotangent bundle T^* M of a pseudo-Riemannian manifold induced by its metric tensor.
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Omega
Omega (capital: Ω, lowercase: ω; Greek ὦ, later ὦ μέγα, Modern Greek ωμέγα) is the 24th and last letter of the Greek alphabet.
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Orthogonal group
In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.
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Orthogonal transformation
In linear algebra, an orthogonal transformation is a linear transformation T: V → V on a real inner product space V, that preserves the inner product.
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Parity (physics)
In quantum mechanics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Polar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
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Pseudoscalar
In physics, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not.
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Pseudovector
In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but in three dimensions gains an additional sign flip under an improper rotation such as a reflection.
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Radian
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.
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Radian per second
The radian per second (symbol: rad·s−1 or rad/s) is the SI unit of rotational speed (angular velocity), commonly denoted by the Greek letter ω (omega).
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Right-hand rule
In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation conventions for the vector cross product in three dimensions.
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Rigid body
In physics, a rigid body is a solid body in which deformation is zero or so small it can be neglected.
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Rigid body dynamics
Rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.
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Rotation
A rotation is a circular movement of an object around a center (or point) of rotation.
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Rotation group SO(3)
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R3 under the operation of composition.
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Rotation matrix
In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
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Skew-symmetric matrix
In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative; that is, it satisfies the condition In terms of the entries of the matrix, if aij denotes the entry in the and; i.e.,, then the skew-symmetric condition is For example, the following matrix is skew-symmetric: 0 & 2 & -1 \\ -2 & 0 & -4 \\ 1 & 4 & 0\end.
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Three-dimensional space
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).
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University of Nottingham
The University of Nottingham is a public research university in Nottingham, United Kingdom.
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Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
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Versor
In mathematics, a versor is a quaternion of norm one (a unit quaternion).
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Vorticity
In continuum mechanics, the vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow.
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Redirects here:
Angular Velocity, Angular speed, Angular velocities, Angular velocity tensor, Rotation velocity.
References
[1] https://en.wikipedia.org/wiki/Angular_velocity
