Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

Thus, at a given angular rate of rotation, a concave surface represents the stable situation, and the more rapid the rotation, the more concave this surface.

where θ is the angle between the vectors Ω < sub > P </ sub > and L. Thus, if the gyroscope's spin slows down ( for example, due to friction ), its angular momentum decreases and so the rate of precession increases.

Thus, the magnitude of the angular velocity vector at a given time t is consistent with the two dimensions case.

Thus, the time travel mechanism would also have to provide instantaneous teleportation, with infinitely accurate and simultaneous adjustment of final 3D location, linear momentum, and angular momentum.

Thus thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and charge of the black hole ( the no-hair theorem ).

Thus the corners become rounded, because angular edges provide more than one area of attack by exposing a greater amount of surface area.

Thus, the position of a rigid body has two components: linear and angular, respectively.

Thus, measuring 180 ° along the angular direction you would encounter a half wave, so the mode number in the angular direction is 1.

Thus, angular magnification is given by:

Thus a low DOP value represents a better GPS positional precision due to the wider angular separation between the satellites used to calculate a GPS unit's position.

Thus, the tangent half-angle formulae give conversions between the stereographic coordinate t on the unit circle and the standard angular coordinate φ.

) Thus, v is a constant, and the velocity vector v also rotates with constant magnitude v, at the same angular rate ω.

Thus, measurements of this angular scale allow an estimation of Ω < sub > 0 </ sub >.

Thus, in the Kepler problem, the angular momentum of a planet about the sun is conserved and the areal velocity is a vector of constant magnitude perpendicular to the orbital plane.

Thus a disc rotating at 60 revolutions per minute ( rpm ) is said to be rotating at either 2π rad / s or 1 Hz, where the former measures the angular velocity and latter reflects the number of complete revolutions per second.

Thus the event duration is determined by the time it takes the apparent motion of the lens in the sky to cover an angular distance.

Thus, certain color contrasts may look fuzzier than others, depending on the allocation of the primary colors ( green has twice as many elements as red or blue in the Bayer arrangement ).

Thus, X-ray diffraction results from an electromagnetic wave ( the X-ray ) impinging on a regular array of scatterers ( the repeating arrangement of atoms within the crystal ).

Thus, the Kaldor test supposes that losers could prevent the arrangement and asks whether gainers value their gain so much they would and could pay losers to accept the arrangement, whereas the Hicks test supposes that gainers are able to proceed with the change and asks whether losers consider their loss to be worth less than what it would cost them to pay gainers to agree not to proceed with the change.

Thus a large number of works exist for the arrangement of piano, violin and violoncello which are not generally titled or numbered as piano trios, but which are nonetheless part of the overall genre.

Thus, in its original context, shading means more than just dark-light arrangement, it is the basis for the beautiful nuance in tonality unique to East Asian ink wash painting and brush-and-ink calligraphy.

Thus, every contentum of the book comes under one or more of these headings, and this methodical arrangement serves to make the exposition clear.

Thus, the correct room acoustics and arrangement of the equipment inside a mastering studio is an important factor since the mastering engineer ( ME ) needs to hear each mix in detail.

Thus, the personal union which had existed for over a century between Britain and Hanover came to an end along with the arrangement of Hanover's ruler living in England as the British and Colonies monarch and using a viceroy to represent them in the German territory.

Thus they reproached him because he wrote in Hebrew instead of in the customary Talmudic idiom, because he departed from the Talmudic order and introduced a division and arrangement of his own, and because he dared to sometimes decide according to the Tosefta and the Jerusalem Talmud as against the Babylonian Talmud.

Thus the colors produced vary with viewing angle, however they are actually surprisingly uniform, perhaps due to the tetrahedral ( diamond-like ) structural arrangement of the scales or diffraction from overlying cell layers.

Thus showing a reproduction of the available, intermediation and arrangement.

Thus, the right side of the brain receives somatosensory input from the left side of the body, and visual input from the left side of the visual field — an arrangement that presumably is helpful for visuomotor coordination.

Thus, members of a non-institutional church would not authorize giving church funds to a missionary society or undertake a " sponsoring church " arrangement, a non-institutional church may send money to an individual preacher, as there are New Testament examples of this (; ; ).

Thus, many Jews supported the American Revolution of 1776, the French Revolution of 1789, and the European Revolutions of 1848 ; while Jews in England tended to vote for the Liberal Party, which had led the parliamentary struggle for Jewish Emancipation — an arrangement called by some scholars “ the liberal Jewish compromise ”.

Thus this Western " proa " often diverged radically from the traditional " proa " to the point that the only shared feature was the windward / leeward hull arrangement.

Thus, the new single-chamber National Assembly dropped the prior traditional arrangement of the bifurcation of legislative powers between a Chamber of Deputies and a Senate.

Thus, as the Tunisian Socialist Destour Party resisted the union plans due to their view that the arrangement was not clear enough and did not include how political institutions would be structured, Bourguiba rescinded on his decision to form the Arab Islamic Republic.

Thus Moronobu's adoption of a grouping of 12 was conventional enough, particularly as such an arrangement afforded a context in which to alter the furnishings, clothing, and design patterns, matched more or less to the months of the year.

Thus, instead of the usual E-A-D-G arrangement, his bass is strung as B-E-A-D.

Thus if you have more than one subject in your picture, the suggestion is to choose an arrangement with at least three subjects.

Thus switching from the Mini type in-sump gearbox arrangement used also in the 204 and 304 to the now-universal end-on gearbox configuration ( pioneered by the Autobianchi Primula ), of front-wheel drive with a transverse engine and a gearbox on the end of the engine and unequal-length drive shafts.

Thus in little more than a hundred years the structural arrangement by provinces envisaged by the First Council of Nicaea was, according to John H. Erickson, transformed into a system of five large divisions headed by the bishops of Rome, Constantinople, Alexandria, Antioch, and Jerusalem.

Thus, passenger engines like the so-called Long Boiler locomotives were usually of a 4-2-0 wheel arrangement.