Elements of Natural Philosophy, Volume 1 |
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Page 62
... Couple is a pair of equal forces acting in dissimilar direc- tions in parallel lines . The Moment of a couple is the sum of the moments of its forces about any point in their plane , and is therefore equal to the product of either force ...
... Couple is a pair of equal forces acting in dissimilar direc- tions in parallel lines . The Moment of a couple is the sum of the moments of its forces about any point in their plane , and is therefore equal to the product of either force ...
Page 63
... couple , upon a body turning about an axis , is the product of the moment of either into the angle ( in circular measure ) through which the body acted on turns , if the moment remains the same in all positions of the DYNAMICAL LAWS AND ...
... couple , upon a body turning about an axis , is the product of the moment of either into the angle ( in circular measure ) through which the body acted on turns , if the moment remains the same in all positions of the DYNAMICAL LAWS AND ...
Page 64
... couple . The proof is obvious . 207. Work done on a body by a force is always shown by a cor- responding increase of vis viva , or kinetic energy , if no other forces act on the body which can do work or have work done against them . If ...
... couple . The proof is obvious . 207. Work done on a body by a force is always shown by a cor- responding increase of vis viva , or kinetic energy , if no other forces act on the body which can do work or have work done against them . If ...
Page 72
... couple about that axis . Hence a constant couple gives uniform acceleration of angular Couple By § 178 we see that the corresponding Mk2 velocity ; or = formula for linear acceleration is s = v = Force M ' 237. For every rigid body ...
... couple about that axis . Hence a constant couple gives uniform acceleration of angular Couple By § 178 we see that the corresponding Mk2 velocity ; or = formula for linear acceleration is s = v = Force M ' 237. For every rigid body ...
Page 128
... couple tending to turn the bar , and W its weight , we have Q = Wa2 sin 0 √1 4a2 8 2 12 sin2 which gives the couple in terms of the deflection 0 . If the torsion of the fibres be taken into account , it will be sensibly equal to ...
... couple tending to turn the bar , and W its weight , we have Q = Wa2 sin 0 √1 4a2 8 2 12 sin2 which gives the couple in terms of the deflection 0 . If the torsion of the fibres be taken into account , it will be sensibly equal to ...
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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 cloth co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance elements ellipse ellipsoid elongation equal equations equilibrium external point Extra fcap finite 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 Natural Philosophy normal section Oxford P₁ parallel particle path pendulum perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular resultant 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 theory tion torsion uniform unit vertical whole wire
Popular passages
Page 161 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Page 65 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force to change that state.
Page 28 - Fourier's theorem is not only one of the most beautiful results of modern analysis, but may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.
Page 161 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Page 66 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.
Page 68 - To every action there is always an equal and contrary reaction; or, the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.
Page 130 - UNTIL we know thoroughly the nature of matter and the forces which produce its motions, it will be utterly impossible to submit to mathematical reasoning the exact conditions of any physical question.