Elements of Natural Philosophy, Volume 1 |
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Page 13
... radius - vector are proportional to the times ; for , as we have seen , the moment of the velocity is double the area traced out by the radius - vector in unit of time . 48. Hence in this case the velocity at any point is inversely as ...
... radius - vector are proportional to the times ; for , as we have seen , the moment of the velocity is double the area traced out by the radius - vector in unit of time . 48. Hence in this case the velocity at any point is inversely as ...
Page 15
... radius - vector is pro- portional to that perpendicular to a fixed line : and therefore the radius - vector of any point is proportional to the distance of that point from a fixed line - a property belonging exclusively to the conic ...
... radius - vector is pro- portional to that perpendicular to a fixed line : and therefore the radius - vector of any point is proportional to the distance of that point from a fixed line - a property belonging exclusively to the conic ...
Page 16
... radius ; being an angle of nearly . П = 57 ° 29578 ... = 57 ° 17′44 ′′ .8 56. The angular velocity of a point in a plane is evidently to be found by dividing the velocity perpendicular to the radius - vector by the length of the radius ...
... radius ; being an angle of nearly . П = 57 ° 29578 ... = 57 ° 17′44 ′′ .8 56. The angular velocity of a point in a plane is evidently to be found by dividing the velocity perpendicular to the radius - vector by the length of the radius ...
Page 17
... radius - vector ; and therefore . ( § 59 ) directly as the angular velocity . Hence the arc of PQ , described in any time , is proportional to the corresponding angle - vector in the orbit , i.e. to the angle through which the tangent ...
... radius - vector ; and therefore . ( § 59 ) directly as the angular velocity . Hence the arc of PQ , described in any time , is proportional to the corresponding angle - vector in the orbit , i.e. to the angle through which the tangent ...
Page 21
... radius is described . V72 Qo For in the fig . , the acceleration of Q ( by § 36 ) is along QO , Supposing , for a moment , QO to represent the magnitude of this ac- celeration , we may resolve it into QP , PO . The acceleration of P is ...
... radius is described . V72 Qo For in the fig . , the acceleration of Q ( by § 36 ) is along QO , Supposing , for a moment , QO to represent the magnitude of this ac- celeration , we may resolve it into QP , PO . The acceleration of P is ...
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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