A Collection of Problems in Illustration of the Principles of Theoretical Mechanics |
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Page vii
... Moment of Inertia 346 I. II . A Material Curve revolving about an 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 ...
... Moment of Inertia 346 I. II . A Material Curve revolving about an 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 ...
Page 13
... moments of the area pqp'q ' about the axes of y and x ; the expressions r2 cos ( π — 0 ) do dr , - r2 sin ( T0 ) de dr , - the moments of the area SPQ about the axes of y and the expressions SS x ; and B fr sin ( T0 ) do dr , r2 cos ( π ...
... moments of the area pqp'q ' about the axes of y and x ; the expressions r2 cos ( π — 0 ) do dr , - r2 sin ( T0 ) de dr , - the moments of the area SPQ about the axes of y and the expressions SS x ; and B fr sin ( T0 ) do dr , r2 cos ( π ...
Page 53
... moment of A ' about O'A ' , and the sum of all such moments for all the forces of the system will be denoted by ( ' a ' ) , those moments being considered positive which tend to twist the body about O'A ' in one direction , and those ...
... moment of A ' about O'A ' , and the sum of all such moments for all the forces of the system will be denoted by ( ' a ' ) , those moments being considered positive which tend to twist the body about O'A ' in one direction , and those ...
Page 54
... Moments . The latter theory , in the case of weights acting at right angles to the arms of a straight lever , was esta- blished by Archimedes ' . In the year 1499 , the condition of equilibrium of a force acting obliquely on a lever ...
... Moments . The latter theory , in the case of weights acting at right angles to the arms of a straight lever , was esta- blished by Archimedes ' . In the year 1499 , the condition of equilibrium of a force acting obliquely on a lever ...
Page 55
... ...... - and , taking moments about the point C , or R. 2a sin a + Wa cos a - R ' . 2a cos a = 0 , 2R sin a + W cos a = 2R ' cos a . ...... . ( 1 ) ; ... . ( 2 ) ; ( 3 ) . From ( 1 ) , ( 2 ) , ( EQUILIBRIUM OF A SINGLE BODY . 55.
... ...... - and , taking moments about the point C , or R. 2a sin a + Wa cos a - R ' . 2a cos a = 0 , 2R sin a + W cos a = 2R ' cos a . ...... . ( 1 ) ; ... . ( 2 ) ; ( 3 ) . From ( 1 ) , ( 2 ) , ( EQUILIBRIUM OF A SINGLE BODY . 55.
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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 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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