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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  • 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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  • 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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  • 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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  • 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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