Elements of Natural Philosophy, Volume 1 |
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Page 36
... denote a plane of the body , the two positions of which are parallel . Move the body from its first position , without rotation , in a direction perpendicular to S , till S comes into the plane of its second position . Then to get the ...
... denote a plane of the body , the two positions of which are parallel . Move the body from its first position , without rotation , in a direction perpendicular to S , till S comes into the plane of its second position . Then to get the ...
Page 38
... denoted by is the angular velocity of the precession , or , as it is sometimes called , the rate of precession . The angular motions w , are to one another inversely as the distances of a point in the axis of the rolling cone from the ...
... denoted by is the angular velocity of the precession , or , as it is sometimes called , the rate of precession . The angular motions w , are to one another inversely as the distances of a point in the axis of the rolling cone from the ...
Page 82
... are equalized they move as one mass with a momentum equal to the sum of the momenta of the two before impact . That is to say , if v denote the common velocity at this instant , we have or ( M + M ' ) v = MV 82 PRELIMINARY .
... are equalized they move as one mass with a momentum equal to the sum of the momenta of the two before impact . That is to say , if v denote the common velocity at this instant , we have or ( M + M ' ) v = MV 82 PRELIMINARY .
Page 83
... denote this proportion , to which we give the name Co - efficient of Restitution1 ; and , with previous nota- tion , let in addition U , U denote the velocities of the two bodies after the conclusion of the impact ; in the standard case ...
... denote this proportion , to which we give the name Co - efficient of Restitution1 ; and , with previous nota- tion , let in addition U , U denote the velocities of the two bodies after the conclusion of the impact ; in the standard case ...
Page 99
... denotes the radius of that circle , w the angular velocity T W a a in it , and b the radius of the circular cross section of the ring . This is proved by remarking that an infinitely narrow band from the outer- most part of the ring has ...
... denotes the radius of that circle , w the angular velocity T W a a in it , and b the radius of the circular cross section of the ring . This is proved by remarking that an infinitely narrow band from the outer- most part of the ring has ...
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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.