A Treatise on DynamicsBell and Company, 1893 - 448 páginas |
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Página 11
... path of the moving point , the angular velocity of the tangent at the point = do do ds = dt ds dt = v ρ where p is the radius of curvature , at the point , of the path . 8. Expressions for accelerations . If x , y are the coordinates ...
... path of the moving point , the angular velocity of the tangent at the point = do do ds = dt ds dt = v ρ where p is the radius of curvature , at the point , of the path . 8. Expressions for accelerations . If x , y are the coordinates ...
Página 17
... If P is the moving point , and if PT , the tangent to its path , is inclined at the angle 0 to Ox , cos e dx = and sin ds = dy ds B. D. 2 The component accelerations parallel to x and y being . TANGENTIAL AND NORMAL ACCELERATIONS . 17.
... If P is the moving point , and if PT , the tangent to its path , is inclined at the angle 0 to Ox , cos e dx = and sin ds = dy ds B. D. 2 The component accelerations parallel to x and y being . TANGENTIAL AND NORMAL ACCELERATIONS . 17.
Página 22
... spiral with the same angular velocity round P ; it is required to find the path of Q. G T સ If a is the angle of the spiral , we have r = acota , and s = sec a.r = rẻ cosec a , so that , if μOP be the velocity of P 22 PHORONOMY .
... spiral with the same angular velocity round P ; it is required to find the path of Q. G T સ If a is the angle of the spiral , we have r = acota , and s = sec a.r = rẻ cosec a , so that , if μOP be the velocity of P 22 PHORONOMY .
Página 23
... path of Q is an equal spiral . - ( 2 ) A circle rolls uniformly inside a circle of double its radius ; it is required to find the acceleration of any carried point . If P be the carried point on the radius CB , and if OB produced meet ...
... path of Q is an equal spiral . - ( 2 ) A circle rolls uniformly inside a circle of double its radius ; it is required to find the acceleration of any carried point . If P be the carried point on the radius CB , and if OB produced meet ...
Página 25
... path . When at A , P has no velocity , and when Q is the point of contact , and is therefore the instantaneous centre , the velocity of P is w . PQ perpendicular to PQ . Taking PQ as an infinitesimal arc , and E as the centre of ...
... path . When at A , P has no velocity , and when Q is the point of contact , and is therefore the instantaneous centre , the velocity of P is w . PQ perpendicular to PQ . Taking PQ as an infinitesimal arc , and E as the centre of ...
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Términos y frases comunes
acting forces action angular momentum axes ball body centre of force centre of gravity chain circle circular component constant coordinates cos² curve cycloid described determine the motion diameter direction of motion disc distance ds ds Edition elastic string ellipse equal equations of motion equilibrium Fcap fixed point given h₁ heavy particle Hence hodograph horizontal plane hyperbola impulses inclination initial instant kinetic energy latus rectum mass moment of inertia momenta natural length normal obtain orbit parabola particle moves path perpendicular point moves position prove radius of curvature radius vector relative revolve ring rotation shew sin² smooth horizontal plane sphere straight line surface Taking tangent tension time-flux tube uniform angular velocity uniformly vertex vertical plane weight
Pasajes populares
Página 48 - 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.