Elements of Natural Philosophy, Volume 1 |
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Page 2
... curvature . Hence the curvature of a circle is in- versely as its radius , and is measured , in terms of the proper unit of curvature , simply by the reciprocal of the radius . 0 I - = - S r is the 10. Any small portion of a curve may ...
... curvature . Hence the curvature of a circle is in- versely as its radius , and is measured , in terms of the proper unit of curvature , simply by the reciprocal of the radius . 0 I - = - S r is the 10. Any small portion of a curve may ...
Page 3
... curvature , in the other a gauche polygon . The term curve of double curvature ' is a very bad one , and , though in very general use , is , we hope , not inera- dicable . The fact is , that there are not two curvatures , but only a ...
... curvature , in the other a gauche polygon . The term curve of double curvature ' is a very bad one , and , though in very general use , is , we hope , not inera- dicable . The fact is , that there are not two curvatures , but only a ...
Page 5
... of the centres of the circles which have at each point the same tangent and curvature as the curve PQ . And we may merely mention , as an obvious result of the B mode of tracing , that the arc qp is equal KINEMATICS . S.
... of the centres of the circles which have at each point the same tangent and curvature as the curve PQ . And we may merely mention , as an obvious result of the B mode of tracing , that the arc qp is equal KINEMATICS . S.
Page 10
... curvature ( perpendicular therefore to the direction of mo- tion ) , whose magnitude is proportional to the square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only ...
... curvature ( perpendicular therefore to the direction of mo- tion ) , whose magnitude is proportional to the square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only ...
Page 17
... curvature of PQ is constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely as the square of the ...
... curvature of PQ is constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely as the square of the ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant cord corresponding 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 formulae friction geometrical given force Hence hodograph horizontal inclined infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ parallel particle path pendulum perpendicular plane perpendicular portion position 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 tion torsion uniform unit vertical weight whole wire