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For two-dimensional rotational motion, Newton's second law can be adapted to describe the relation between torque and angular acceleration:
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For and two-dimensional
For a two-dimensional array, the element with indices i, j would have address B + c · i + d · j, where the coefficients c and d are the row and column address increments, respectively.
For example, a similar geometric system was published in 1987 by Kjell Gustafson, whose method represents a rhythm as a two-dimensional graph.
For convenience, pixels are normally arranged in a regular two-dimensional grid.
For example, Girih tiles in a medieval Islamic mosque in Isfahan, Iran, are arranged in a two-dimensional quasicrystalline pattern.
For example, the surface of the Earth is ( ideally ) a two-dimensional sphere, and latitude and longitude provide two-dimensional coordinates on it ( except at the poles and along the 180th meridian ).
For a two-dimensional situation with horizontal and vertical forces, the sum of the forces requirement is two equations: ΣH
For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional ( 2D ) surface.
For two-dimensional signals, e. g., images, the spectrum is reciprocal to f < sup > 2 </ sup >.
For example, is a meromorphic function on the two-dimensional complex affine space.
For a two-dimensional surface, the Bianchi identities imply that the Riemann tensor can be expressed as
For example, atmospheric cyclones are rotational but their substantially two-dimensional shapes do not allow vortex generation and so are not turbulent.
For example, the ordinary generating function of a two-dimensional array a < sub > m, n </ sub > ( where n and m are natural numbers ) is
For instance, a "< big > b </ big >" and a "< big > d </ big >" have a different shape, at least when they are constrained to move within a two-dimensional space like the page on which they are written.
For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.
For convex two-dimensional shapes, the centroid can be found by balancing the shape on a smaller shape, such as the top of a narrow cylinder.
For example, a monatomic gas with a fixed number of particles is a simple case of a two-dimensional system ().
For instance, in the BF model, the spacetime is a two-dimensional manifold M, the observables are constructed from a two-form F, an auxiliary scalar B, and their derivatives.
For a two-dimensional flow the vorticity acts as a measure of the local rotation of fluid elements.
For a two-dimensional analysis a plane stress or a plane strain condition can be assumed.
For example, Kahane uses Cantor sets to construct a Besicovitch set of measure zero in the two-dimensional plane.
For such models, economists often use two-dimensional graphs instead of functions.
For example, a two-dimensional real torus has a SL ( 2, Z ) group of large diffeomorphisms by which the one-cycles of the torus are transformed into their integer linear combinations.
For the graph of a two-dimensional function, this corresponds to a point on the graph where the tangent plane is parallel to the xy plane.
For and rotational
For example, the increase in rotational speed of a spinning figure skater as the skater's arms are contracted is a consequence of conservation of angular momentum.
For fluorophores in solution this means that the intensity and polarization of the emitted light is dependent on rotational diffusion.
For an nk-gon with k-fold rotational symmetry ( C < sub > k </ sub >), there are degrees of freedom for the shape.
For example, there are many common lasers ( e. g., dye lasers, carbon dioxide lasers ) where the laser medium consists of complete molecules, and energy states correspond to vibrational and rotational modes of oscillation of the molecules.
For example, a rotational force applied to a shaft causing acceleration, such as a drill bit accelerating from rest, the resulting moment is called a torque.
For example, if rotational speed ( revolutions per time ) is used in place of angular speed ( radians per time ), we multiply by a factor of 2π radians per revolution.
For multi-rotational jumps, it is important that the skater assume a " tight " position in the air by holding the arms close to the body, to concentrate their body mass around the axis of rotation and minimize the rotational moment of inertia.
For a system composed of simple lenses and mirrors, the axis passes through the center of curvature of each surface, and coincides with the axis of rotational symmetry.
For dihydrogen, each nucleus is a proton of spin 1 / 2, so that it can be shown using quantum mechanics and the Pauli exclusion principle that the odd rotational levels are more populated than the even levels.
For a bullet, the specific formula below uses the bullet's MV and the barrel's twist rate to calculate rotational speed:
For a function from a space X to itself, or for an operator that acts on such functions, rotational invariance may also mean that the function or operator commutes with rotations of X.
For a ( rigid ) rectangular transparent sheet, inversion symmetry corresponds to having on one side an image without rotational symmetry and on the other side an image such that what shines through is the image at the top side, upside down.
For six weeks in May and June 1940 the station was home to No. 222 Squadron RAF on a rotational rest and recuperation break from fighting the Battle of Britain from RAF Duxford.
For a linear molecule, the separation of lines in the rotational spectrum can be related directly to the moment of inertia of the molecule, and, for a molecule of known atomic masses, can be used to determine the bond lengths ( structure ) directly.
For diatomic molecules, this process is trivial, and can be made from a single measurement of the rotational spectrum.
For radar dishes, a single, large, ball-shaped dome also protects the rotational mechanism and the sensitive electronics, and is heated in colder climates to prevent icing.
For very small mass differences between m < sub > 1 </ sub > and m < sub > 2 </ sub >, the rotational inertia I of the pulley of radius r cannot be neglected.
For infinite cones, the word axis again usually refers to the axis of rotational symmetry ( if any ).
For example, the power produced by an engine, motor or other rotating prime mover can be calculated by simultaneously measuring torque and rotational speed ( RPM ).
For example, a tachometer may use a strobe light with an adjustable PRF to measure rotational velocity.
For example, an object is rotating at 60 revolutions per second: if it is viewed with a series of short flashes at 60 times per second, each flash illuminates the object at the same position in its rotational cycle, so it appears that the object is stationary.
For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance.
For performing rotational tricks on flat ground, frontside means that for the first 90-180 degrees of the rotation, the rider can see ahead in the direction of travel.
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