A Collection of Problems in Illustration of the Principles of Theoretical Mechanics |
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Page 346
... radius of gyration of a circular arc about a radius through its vertex . Let HAK ( fig . 174 ) be the circular arc , 4 its vertex , C the centre of the circle . Take any point P in the arc ; draw PM at right angles to the radius CA ...
... radius of gyration of a circular arc about a radius through its vertex . Let HAK ( fig . 174 ) be the circular arc , 4 its vertex , C the centre of the circle . Take any point P in the arc ; draw PM at right angles to the radius CA ...
Page 347
... radius of gyration of a material straight line OB , ( fig . 175 ) , about an axis OA , to which it is inclined at a given angle , the density at any point of OB varying as some power of its distance from 0 . Take any point Pin OB ; draw ...
... radius of gyration of a material straight line OB , ( fig . 175 ) , about an axis OA , to which it is inclined at a given angle , the density at any point of OB varying as some power of its distance from 0 . Take any point Pin OB ; draw ...
Page 348
... radius of gyration of a straight line AB , ( fig . 176 ) about an axis through D at right angles to the plane ADB . = Let C be the middle point of the line ; join CD . Let AC = a = BC , CD = b ; k = the radius of gyration about the axis ...
... radius of gyration of a straight line AB , ( fig . 176 ) about an axis through D at right angles to the plane ADB . = Let C be the middle point of the line ; join CD . Let AC = a = BC , CD = b ; k = the radius of gyration about the axis ...
Page 349
... radius of gyration of an elliptic area , of uniform thickness and density , about its principal axes . Let p ... radius of gyration about the axis b , we shall have , by similar reasoning , k " 2 = fa2 . ( 2 ) To find the radius of ...
... radius of gyration of an elliptic area , of uniform thickness and density , about its principal axes . Let p ... radius of gyration about the axis b , we shall have , by similar reasoning , k " 2 = fa2 . ( 2 ) To find the radius of ...
Page 350
William Walton. ( 2 ) To find the radius of gyration of a circular area revolving about a straight line parallel to its plane , at a distance c from its centre . If a be the radius of the circle , and k the required radius of gyration ...
William Walton. ( 2 ) To find the radius of gyration of a circular area revolving about a straight line parallel to its plane , at a distance c from its centre . If a be the radius of the circle , and k the required radius of gyration ...
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Common terms and phrases
absolute force acted angular velocity attraction axes axis body catenary centre of force centre of gravity circle co-ordinates coefficient of friction cos² curve cylinder d²x denote density descends determine direction distance dr² dt dt dt² dx dy dx² elastic ellipse equal equation Euler find the centre fixed point formula given velocity hence horizontal plane inclined plane inertia initial value integrating James Bernoulli John Bernoulli length ma² mass moment of inertia motion oscillation parabola particle perpendicular position of equilibrium pressure problem projection radius of gyration resistance rest right angles Sciences de Paris SECT shews sin² sphere straight line string supposing surface taking moments tan² tangent tension triangle tube vertical plane Vis Viva weight zero δε аф
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