A Collection of Problems in Illustration of the Principles of Theoretical Mechanics |
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Page vii
... Axis within its own Plane A Material Line revolving about an Axis at Right Angles to its own Plane 346 348 III . A Plane Area revolving about an Axis within or parallel to the Plane . 349 IV . Plane Area about a Perpendicular Axis 350 V ...
... Axis within its own Plane A Material Line revolving about an Axis at Right Angles to its own Plane 346 348 III . A Plane Area revolving about an Axis within or parallel to the Plane . 349 IV . Plane Area about a Perpendicular Axis 350 V ...
Page 3
... axis of the parabola . Then , Px and Py being taken as the axes of x and y , the equation to the curve will be y ' = 4mx , m being the distance of the point P from the focus . Hence , if PE = a , xy dx ៤ ៖ fryde fade 4 Syde fade dx 0 ...
... axis of the parabola . Then , Px and Py being taken as the axes of x and y , the equation to the curve will be y ' = 4mx , m being the distance of the point P from the focus . Hence , if PE = a , xy dx ៤ ៖ fryde fade 4 Syde fade dx 0 ...
Page 8
... axis of y , and the conjugate diameter as the axis of x , the equation to the ellipse will be and we shall have y3 = — ( a2 — x2 ) , 4a x = 3π · Guldin ; Centrobaryca , Lib . I. cap . 9 , p . 115 . ( 8 ) To find the centre of gravity of ...
... axis of y , and the conjugate diameter as the axis of x , the equation to the ellipse will be and we shall have y3 = — ( a2 — x2 ) , 4a x = 3π · Guldin ; Centrobaryca , Lib . I. cap . 9 , p . 115 . ( 8 ) To find the centre of gravity of ...
Page 15
... axis of x ; then the centre of gravity will be within the axis of x , its position being given by the formula ffxy [ [ xy dady fx ( y2 — [ x - y " ) de dx [ [ ydxdy [ ( y2 ( y2 - y ) dz dx y , y ' , being the limiting values of y for ...
... axis of x ; then the centre of gravity will be within the axis of x , its position being given by the formula ffxy [ [ xy dady fx ( y2 — [ x - y " ) de dx [ [ ydxdy [ ( y2 ( y2 - y ) dz dx y , y ' , being the limiting values of y for ...
Page 21
... axis of the paraboloid as the axis of z ; also let the axis of x be so taken that the plane of zx coincides with the bisecting plane ; and take the axis of y at right angles to this plane . Then , if a be the radius of the sphere , the ...
... axis of the paraboloid as the axis of z ; also let the axis of x be so taken that the plane of zx coincides with the bisecting plane ; and take the axis of y at right angles to this plane . Then , if a be the radius of the sphere , the ...
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Other editions - View all
A Collection of Problems in Illustration of the Principles of Theoretical ... William Walton No preview available - 2018 |
A Collection of Problems in Illustration of the Principles of Theoretical ... William Walton No preview available - 2017 |
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 collision cos² curve cylinder d²x denote density determine direction distance dx dy dx² elastic ellipse equal equation Euler find the centre find the position fixed point formula given velocity hence horizontal plane inclined plane integrating James Bernoulli John Bernoulli latus rectum middle point motion oscillation parabola particle perpendicular position of equilibrium pressure problem projection radius of gyration rest right angles SECT shews sin² smooth sphere square straight line string supposing surface taking moments tan² tangent tension triangle tube unit of mass varying inversely vertical plane virtual velocities Vis Viva weight zero
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