Elements of Natural Philosophy |
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Page 8
... square root of the sum of their squares ; and the cosines of its inclination to the given directions are the ratios of the components to the resultant . 32. The velocity of a point is said to be accelerated or retarded according as it ...
... square root of the sum of their squares ; and the cosines of its inclination to the given directions are the ratios of the components to the resultant . 32. The velocity of a point is said to be accelerated or retarded according as it ...
Page 10
... square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only the form of the path , or the direction of motion . Hence if a moving point be subject to an acceleration ...
... square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only the form of the path , or the direction of motion . Hence if a moving point be subject to an acceleration ...
Page 14
... square of the periodic time [ in an elliptic orbit ] is pro- portional to the cube of the major axis . Sections 45-47 , taken in connexion with the second of these laws , show that the acceleration of the motion of a planet or comet is ...
... square of the periodic time [ in an elliptic orbit ] is pro- portional to the cube of the major axis . Sections 45-47 , taken in connexion with the second of these laws , show that the acceleration of the motion of a planet or comet is ...
Page 17
... square of the distance from this point . The same proposition is true for any path , when the acceleration is towards the point about which the angles are measured : being merely a different mode of stating the result of § 48 . 60. The ...
... square of the distance from this point . The same proposition is true for any path , when the acceleration is towards the point about which the angles are measured : being merely a different mode of stating the result of § 48 . 60. The ...
Page 37
... square of the resultant angular velocity is the sum of the squares of its components , and the ratios of the three components to the resultant are the direction - cosines of the axis . Hence also , an angular velocity about any line may ...
... square of the resultant angular velocity is the sum of the squares of its components , and the ratios of the three components to the resultant are the direction - cosines of the axis . Hence also , an angular velocity about any line may ...
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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 cord corresponding 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 formulae friction geometrical given force Hence hodograph horizontal inclined infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ parallel parallelogram particle path pendulum perpendicular plane perpendicular portion position pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular relative 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 tion torsion uniform unit vertical weight whole wire