Radius-of-curvature sentence example

radius-of-curvature
  • The same method of representation is applicable to spherical waves, issuing from a point, if the radius of curvature be large; for, although there is variation of phase along the length of the infinitesimal strip, the whole effect depends practically upon that of the central parts where the phase is sensibly constant.'
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  • The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.
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  • if r denotes the radius of curvature of the stream line, so that I dp + dV - dH _ dq 2 q2 (6) p dv dv dv dv - r ' the normal acceleration.
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  • Along the path of a particle, defined by the of (3), _ c) sine 2e, - x 2 + y2 = y a 2 ' (Io) sin B' de' _ 2y-c dy 2 ds ds' on the radius of curvature is 4a 2 /(ylc), which shows that the curve is an Elastica or Lintearia.
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  • At any point a sounding line would hang in the line of the radius of curvature of the water surface.
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  • If w is the weight of a locomotive in tons, r the radius of curvature of the track, v the velocity in feet per sec.; then the horizontal force exerted on the bridge is wv 2 /gr tons.
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  • Then the deflection at the centre is the value of y for x = a, and is _ 5 wa4 S - 14 EI' The radius of curvature of the beam at D is given by the relation R=EI/M.
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  • P we have (T + T) sin ai,L, or T4~, or Ts/p, where p is the radius of curvature.
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  • ~ the inclination to the horizontal at A or B, we have 2T~=W, AB =2p~t, approximately, where p is the radius of curvature.
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  • where p is the radius of curvature of the path at P, the tangential and normal accelerations are also expressed by v dv/ds and v1/p, respectively.
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  • Nearly Epicycloidal Teeth: Williss Method.To facilitate the drawing of epicycloidal teeth in practice, Willis showed how to approximate to their figure by means of two circular arcsone concave, for the flank, and the other convex, for the faceand each having for its radius the mean radius of curvature of the epicycloidal arc. \Villiss formulae are founded on the following properties of epicycloids Let R be the radius of the pitch-circle; r that of the describing circle; 8 the angle made by the normal TI to the epicycloid at a given point T, with a tangent-to the circle at Ithat is, the obliquity of the action at T.
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  • Then the radius of curvature of the epicycloid at T is For an internal epicycloid, p =4r sin o~1
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  • By comparing this with the expression for the centrifugal force (wap/g), it appears that the actual energy of a revolving body is equal to the potential energy Fp/2 due to the action of the deflecting force along one-half of the radius of curvature of the path of the body.
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  • If we take the axis of z normal to either surface of the film, the radius of curvature of which we suppose to be very great compared with its thickness c, and if p is the density, and x the energy of unit of mass at depth z, then o- = f o dz, (16) and e = f a xpdz,.
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  • section whose radius of curvature is R1.
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  • Suppose that the transition from o to s is made in two equal steps, the thickness of the intermediate layer of density la being large compared to the range of the molecular forces, but small in comparison with the radius of curvature.
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  • (io) Now ds - sin a (II) The radius of curvature of the meridian section is ds R1= a.
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  • (12) d The radius of curvature of a normal section of the surface at right angles to the meridian section is equal to the part of the normal cut off by the axis, which is R2 = PN =y/ cos a (13).
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  • We know that the radius of curvature of a surface of revolution in the plane normal to the meridian plane is the portion of the normal intercepted by the axis of revolution.
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  • The radius of curvature of a catenary is equal and opposite to the portion of the normal intercepted by the directrix of the catenary.
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  • The radius of curvature at any point is readily deduced from the intrinsic equation and has the value p=4 cos 40, and is equal to twice the normal which is 2a cos 2B.
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  • plano-convex lens is placed with its curved surface with radius of curvature R resting on a plane glass surface.
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  • tons, (4) w denoting the density of water in tons/ft.', and W =wV, for a displacement of V ft.3 This couple, combined with the original buoyancy W through B, is equivalent to the new buoyancy through B, so that W.BB 1 =wAk 2 tan 8, (5) BM =BB 1 cot B=Ak e /V, (6) giving the radius of curvature BM of the curve of buoyancy B, in terms of the displacement V, and Ak e the moment of inertia of the water-line area about an axis through F, perpendicular to the plane of displacement.
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  • duced by euclidian methods from the definition include the following: the tangent at any point bisects the angle between the focal distance and the perpendicular on the directrix and is equally inclined to the focal distance and the axis; tangents at the extremities of a focal chord intersect at right angles on the directrix, and as a corollary we have that the locus of the intersection of tangents at right angles is the directrix; the circumcircle of a triangle circumscribing a parabola passes through the focus; the subtangent is equal to twice the abscissa of the point of contact; the subnormal is constant and equals the semilatus rectum; and the radius of curvature at a point P is 2 (FP) 4 /a 2 where a is the semilatus rectum and FP the focal distance of P.
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  • The catenaries which lie between the two whose direction coincides with the axis of revolution generate surfaces whose radius of curvature convex towards the axis in the meridian plane is less than the radius of concave curvature.
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  • The catenaries which lie beyond the two generate surfaces whose radius of curvature convex towards the axis in the meridian plane is greater than the radius of concave curvature.
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  • A shaving or make-up mirror of this type has a radius of curvature of 30 cm.
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