Elements of Natural Philosophy, Volume 1 |
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Page 14
... constant quantity . Other examples of these principles will be met with in the chapters on Kinetics . 49. If , as in § 35 , from any fixed point , lines be drawn at every instant representing in magnitude and direction the velocity of a ...
... constant quantity . Other examples of these principles will be met with in the chapters on Kinetics . 49. If , as in § 35 , from any fixed point , lines be drawn at every instant representing in magnitude and direction the velocity of a ...
Page 15
... constant , the locus of U is easily seen to be a circle . Hence the proposition is generally true for all conic sections . The hodograph surrounds its origin if the orbit be an ellipse , passes through it when the orbit is a para- bola ...
... constant , the locus of U is easily seen to be a circle . Hence the proposition is generally true for all conic sections . The hodograph surrounds its origin if the orbit be an ellipse , passes through it when the orbit is a para- bola ...
Page 17
... constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely as the square of the distance of the moving ...
... constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely as the square of the distance of the moving ...
Page 18
... constant ratio the line joining them . Let A and B be any simultaneous positions of the points . Take G or G ' in AB such that the ratio GA G'A or GB G'B has a constant value . Then , as the form of the relative G A Ꮐ B path depends ...
... constant ratio the line joining them . Let A and B be any simultaneous positions of the points . Take G or G ' in AB such that the ratio GA G'A or GB G'B has a constant value . Then , as the form of the relative G A Ꮐ B path depends ...
Page 22
... constant ( since the angular velocities of CQ and CQ are equal , and therefore the angle QCQ is constant ) , and revolves with the same angular velocity as CQ or CQ ; and therefore the resultant motion is simple harmonic , of amplitude ...
... constant ( since the angular velocities of CQ and CQ are equal , and therefore the angle QCQ is constant ) , and revolves with the same angular velocity as CQ or CQ ; and therefore the resultant motion is simple harmonic , of amplitude ...
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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