Elements of Natural Philosophy, Part 1 |
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Page 71
... Radius of Gyration about the axis from which is measured . The radius of gyration about any axis is therefore the distance from that axis at which , if the whole mass were placed , it would have the same moment of inertia as before . In ...
... Radius of Gyration about the axis from which is measured . The radius of gyration about any axis is therefore the distance from that axis at which , if the whole mass were placed , it would have the same moment of inertia as before . In ...
Page 72
... radius of gyration of the whole . 236. The rate of increase of moment of momentum is thus , in New- ton's notation ... radius - vector is inversely proportional to the radius of gyration of the body about that radius - vector as axis ...
... radius of gyration of the whole . 236. The rate of increase of moment of momentum is thus , in New- ton's notation ... radius - vector is inversely proportional to the radius of gyration of the body about that radius - vector as axis ...
Page 86
... radius of gyration . Then if w be the angular velocity of the pendulum when the impact is complete , mvp = Mk2w , from which the solution of the question is easily determined . For the kinetic energy after impact is changed ( § 207 ) ...
... radius of gyration . Then if w be the angular velocity of the pendulum when the impact is complete , mvp = Mk2w , from which the solution of the question is easily determined . For the kinetic energy after impact is changed ( § 207 ) ...
Page 266
... radius of gyration of the plane area about the axis of x . For the moment about y we have Spxdxdy = App cos a ffxydxdy . The first terms of these three expressions merely give us again the results of § 688 ; we may therefore omit them ...
... radius of gyration of the plane area about the axis of x . For the moment about y we have Spxdxdy = App cos a ffxydxdy . The first terms of these three expressions merely give us again the results of § 688 ; we may therefore omit them ...
Page 267
... radius of gyration of the plane area about a horizontal axis in its plane , and passing through its centre of inertia , we have k2 = k12 + y2 . Hence the distance , measured parallel to the axis of y , of the centre of pressure from the ...
... radius of gyration of the plane area about a horizontal axis in its plane , and passing through its centre of inertia , we have k2 = k12 + y2 . Hence the distance , measured parallel to the axis of y , of the centre of pressure from the ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called Cambridge 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 ellipsoid elongation equal equations equilibrium external 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 Octavo P. G. TAIT P₁ P₂ parallel particle path pendulum perpendicular plane 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 theorem theory tion torsion uniform unit vertical whole wire
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