A Treatise on DynamicsBell and Company, 1893 - 448 páginas |
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Página 40
... proportional to the radial component of its velocity . 13. If the velocities of a point parallel and perpendicular to the radius vector are always proportional to each other , and likewise the accelerations , its velocity will vary as ...
... proportional to the radial component of its velocity . 13. If the velocities of a point parallel and perpendicular to the radius vector are always proportional to each other , and likewise the accelerations , its velocity will vary as ...
Página 41
... proportional to the cube of the velocity . 19. Shew that it is possible for a point to move so that the velocity at any time shall be proportional to the space described from a fixed origin at a time a seconds before , and the ...
... proportional to the cube of the velocity . 19. Shew that it is possible for a point to move so that the velocity at any time shall be proportional to the space described from a fixed origin at a time a seconds before , and the ...
Página 42
... proportional to 1 dp - p ds 25. Prove that the angular acceleration of the direction of motion of a point moving in a plane is v dv v2 dp p ds p2 ds • 26. The position of a point is given by the perpendiculars , n on two fixed lines ...
... proportional to 1 dp - p ds 25. Prove that the angular acceleration of the direction of motion of a point moving in a plane is v dv v2 dp p ds p2 ds • 26. The position of a point is given by the perpendiculars , n on two fixed lines ...
Página 43
... proportional to the velocity in the direction of the other , the path of the particle is given by an equation of the form ( 1 + 1 ) ( 2 ) = = Ar2 + 2D ( A + 1 ) log r ― D 2 + C. 34. An equilateral triangle , ABC , turns in its EXAMPLES .
... proportional to the velocity in the direction of the other , the path of the particle is given by an equation of the form ( 1 + 1 ) ( 2 ) = = Ar2 + 2D ( A + 1 ) log r ― D 2 + C. 34. An equilateral triangle , ABC , turns in its EXAMPLES .
Página 46
... proportional to the perpendicular from the origin on the tangent to the locus at any instant . Prove that they will always lie in a similar curve with the origin for a centre of similitude , and that if they move so as to approach the ...
... proportional to the perpendicular from the origin on the tangent to the locus at any instant . Prove that they will always lie in a similar curve with the origin for a centre of similitude , and that if they move so as to approach the ...
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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.