Elements of Natural Philosophy, Volume 1 |
From inside the book
Results 11-15 of 72
Page 27
... resultant of each group is uniform circular motion . If their periods are equal , we have a case belonging to those already treated ( § 80 ) , and conclude that the resultant is , in general , motion in an ellipse , equal areas being ...
... resultant of each group is uniform circular motion . If their periods are equal , we have a case belonging to those already treated ( § 80 ) , and conclude that the resultant is , in general , motion in an ellipse , equal areas being ...
Page 31
... resultant rotation by the same process . Or we may adopt the following far simpler method : -Let OA be the translation common to B ' all points in the plane , and let BOC be the angle of rotation about O , BO being drawn so that C ...
... resultant rotation by the same process . Or we may adopt the following far simpler method : -Let OA be the translation common to B ' all points in the plane , and let BOC be the angle of rotation about O , BO being drawn so that C ...
Page 35
... resultant axis . Again , if Bb be drawn perpendicular to OA , and if be the angular velocity about OI , the whole displacement of B may evidently be represented either by Hence w.Bb or .IB . : w :: Bb : Iß :: O1 : Op . And thus on the ...
... resultant axis . Again , if Bb be drawn perpendicular to OA , and if be the angular velocity about OI , the whole displacement of B may evidently be represented either by Hence w.Bb or .IB . : w :: Bb : Iß :: O1 : Op . And thus on the ...
Page 48
... non - rotational shear , we must turn CD through an angle P1OP only , which is less than QOQ by the excess of P1OQ above QOP . Hence the resultant of the two 29 shears , PP1 , P ̧Ð1⁄2 , each separately deprived 48 PRELIMINARY .
... non - rotational shear , we must turn CD through an angle P1OP only , which is less than QOQ by the excess of P1OQ above QOP . Hence the resultant of the two 29 shears , PP1 , P ̧Ð1⁄2 , each separately deprived 48 PRELIMINARY .
Page 49
... resultant in a single non - rotational shear : we conclude with the body unstrained , but turned through the angle QOP1 - POQ , in the same direction as the hands of a watch . ] 162. As there can be neither annihilation nor generation ...
... resultant in a single non - rotational shear : we conclude with the body unstrained , but turned through the angle QOP1 - POQ , in the same direction as the hands of a watch . ] 162. As there can be neither annihilation nor generation ...
Other editions - View all
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