Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page 2
... instant the tangent drawn to its path , if the path be a curve , or the path itself if a straight line . 5. If the path be not straight the direction of motion changes from point to point , and the rate of this change , per unit of ...
... instant the tangent drawn to its path , if the path be a curve , or the path itself if a straight line . 5. If the path be not straight the direction of motion changes from point to point , and the rate of this change , per unit of ...
Page 11
... instant ; or it may be variable . Uniform velocity is measured by the space passed over in unit of time , and is , in general , expressed in feet per second ; if very great , as in the case of light , it is sometimes popularly reckoned ...
... instant ; or it may be variable . Uniform velocity is measured by the space passed over in unit of time , and is , in general , expressed in feet per second ; if very great , as in the case of light , it is sometimes popularly reckoned ...
Page 12
... instant of the interval . Or again , we define the exact velocity at any instant as the space which the point would have described in one second , if for one second its velocity remained unchanged . That there is at every instant a ...
... instant of the interval . Or again , we define the exact velocity at any instant as the space which the point would have described in one second , if for one second its velocity remained unchanged . That there is at every instant a ...
Page 18
... instant . 32. In other words , if a point move in a curve , whether with a uniform or a varying velocity , its change of direction is to be regarded as constituting an acceleration towards the centre of curvature , equal in amount to ...
... instant . 32. In other words , if a point move in a curve , whether with a uniform or a varying velocity , its change of direction is to be regarded as constituting an acceleration towards the centre of curvature , equal in amount to ...
Page 19
... instant , or simply its rectangular components , be given , provided the velocity and direction of motion , as well as the position , of the point at any one instant , be given . For we have in the first case dx = u = q cos a , etc ...
... instant , or simply its rectangular components , be given , provided the velocity and direction of motion , as well as the position , of the point at any one instant , be given . For we have in the first case dx = u = q cos a , etc ...
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Common terms and phrases
acceleration action algebraic altered angular velocity anticlastic application axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy length linear momentum moving negative osculating plane P₁ parallel particle perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ λ² аф
Popular passages
Page 241 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.