A Treatise on DynamicsBell and Company, 1893 - 448 páginas |
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Página 40
... described inversely . Prove that the curvature varies inversely as the arc . 7. A wheel revolves uniformly about its centre C , which is fixed , and a particle A moves uniformly in a straight line through the centre ; describe the path ...
... described inversely . Prove that the curvature varies inversely as the arc . 7. A wheel revolves uniformly about its centre C , which is fixed , and a particle A moves uniformly in a straight line through the centre ; describe the path ...
Página 41
... described by P from the beginning of the motion ; shew that the acceleration of the point R is represented in magnitude and direction by RQ . 17. The tangent at a point P of a parabola meets the tangent at the vertex in Y and the axis ...
... described by P from the beginning of the motion ; shew that the acceleration of the point R is represented in magnitude and direction by RQ . 17. The tangent at a point P of a parabola meets the tangent at the vertex in Y and the axis ...
Página 45
... described by P. 41. A plane is moving about an axis perpendicular to it , and a point is moving in a given curve traced on the plane ; in any position is the angular velocity of the plane , v the velocity of the particle relative to the ...
... described by P. 41. A plane is moving about an axis perpendicular to it , and a point is moving in a given curve traced on the plane ; in any position is the angular velocity of the plane , v the velocity of the particle relative to the ...
Página 96
... described , we have the equations , y2 = 2lx — nx2 , = 0 , mimY . From these we obtain - x = c , and yỷ = ( 1 − nx ) c , hence yÿ + y2 = — nc2 , and therefore ÿ = = - 12c2 shewing that the force varies inversely as the cube of the ...
... described , we have the equations , y2 = 2lx — nx2 , = 0 , mimY . From these we obtain - x = c , and yỷ = ( 1 − nx ) c , hence yÿ + y2 = — nc2 , and therefore ÿ = = - 12c2 shewing that the force varies inversely as the cube of the ...
Página 97
... described . In this case , if P be the force , P P mi = √2 ' and my = - √2 * Hence ¿ -y = c , and from the equation of the curve x2 + y2ỷ = 0 . These equations give cy1 Ca2 = x2 + y2 Ў = x2 + y2 ' and 2c2a3xy ( x2 + y2 ) 3 ' whence ...
... described . In this case , if P be the force , P P mi = √2 ' and my = - √2 * Hence ¿ -y = c , and from the equation of the curve x2 + y2ỷ = 0 . These equations give cy1 Ca2 = x2 + y2 Ў = x2 + y2 ' and 2c2a3xy ( x2 + y2 ) 3 ' whence ...
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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.