Elements of Natural Philosophy, Volume 1 |
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Results 6-10 of 66
Page 29
... amount of the angle of rotation . 93. The lines equidistant from A and A ' , and from B and B , áre parallel if AB is parallel to A'B ' ; and therefore the construction fails , the point O being infinitely distant , and the theorem ...
... amount of the angle of rotation . 93. The lines equidistant from A and A ' , and from B and B , áre parallel if AB is parallel to A'B ' ; and therefore the construction fails , the point O being infinitely distant , and the theorem ...
Page 30
... 91 gives us at once the point 0 and the amount of rotation about it which singly gives the same effect as those about A and B in succession . But there is one case of Α ' A B B exception , viz . when 30 PRELIMINARY .
... 91 gives us at once the point 0 and the amount of rotation about it which singly gives the same effect as those about A and B in succession . But there is one case of Α ' A B B exception , viz . when 30 PRELIMINARY .
Page 31
... amount and in opposite directions . In this case A'B ' is evidently parallel to AB , and therefore the compound ... amounts and opposite directions , compound one of them with the given rotation by § 98 , and then compound the other with ...
... amount and in opposite directions . In this case A'B ' is evidently parallel to AB , and therefore the compound ... amounts and opposite directions , compound one of them with the given rotation by § 98 , and then compound the other with ...
Page 34
... amount of rotation about a definite axis . And hence , also , successive or simul- taneous rotations about any number of axes through the fixed point may be compounded into one such rotation . 107. Let OA , OB be two axes about which 34 ...
... amount of rotation about a definite axis . And hence , also , successive or simul- taneous rotations about any number of axes through the fixed point may be compounded into one such rotation . 107. Let OA , OB be two axes about which 34 ...
Page 35
... amounts of these displacements will be wẞ.7 and — wla.T. ωΙα.τ. The point I , and therefore every point in the line OI , will be at rest during the interval τ if the sum of these displacements is zero - i . e . if w1.1ẞ = w.Ia . - b P B ...
... amounts of these displacements will be wẞ.7 and — wla.T. ωΙα.τ. The point I , and therefore every point in the line OI , will be at rest during the interval τ if the sum of these displacements is zero - i . e . if w1.1ẞ = w.Ia . - b P B ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centimetre centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance ellipse ellipsoid elongation equal equations equilibrium external point finite fixed point flexure fluid forces acting friction geometrical given force Hence hodograph horizontal infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ P₂ parallel parallelogram of forces particle path pendulum perpendicular plane perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular right angles rigid body rotation round shear shell sides simple harmonic motion solid angle space spherical surface spiral square straight line strain stress suppose tangent theorem theory tion torsion uniform unit vertical whole wire