Solutions of the Examples Appended to A Treatise on the Motion of a Rigid Body |
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Page 3
... whole length of the line , b + b ' c + c ' = Ꮇ . + 3 m n . R3 , 2 2 − c ' ) \ b ' ) ( c c ' ) ( c - - x { ( b + b ) ( 0 + c ) + ( b − b ) ( ( = ( ) ) . = M - 2 4 12 M { 4 ( be + b'c ' ) + 2 ( bc ' + b'c ) } , = } M { 2 ...
... whole length of the line , b + b ' c + c ' = Ꮇ . + 3 m n . R3 , 2 2 − c ' ) \ b ' ) ( c c ' ) ( c - - x { ( b + b ) ( 0 + c ) + ( b − b ) ( ( = ( ) ) . = M - 2 4 12 M { 4 ( be + b'c ' ) + 2 ( bc ' + b'c ) } , = } M { 2 ...
Page 5
... whole BAC , whose mass is 2 M , will be double that of AB , which is required . Let G be the centre of gravity of BAC . Then 2 Mr2 being the moment of inertia of BAC about an axis perpendicular to its plane through O the centre , moment ...
... whole BAC , whose mass is 2 M , will be double that of AB , which is required . Let G be the centre of gravity of BAC . Then 2 Mr2 being the moment of inertia of BAC about an axis perpendicular to its plane through O the centre , moment ...
Page 21
... whole were collected at the centre of oscillation , since the distance of this point from the axis = ( +1 ) r , the pressure would be Mg + Mrw2 + & Mrw2 , .. difference = & Mrw3 . This example is meant to guard the reader against sup ...
... whole were collected at the centre of oscillation , since the distance of this point from the axis = ( +1 ) r , the pressure would be Mg + Mrw2 + & Mrw2 , .. difference = & Mrw3 . This example is meant to guard the reader against sup ...
Page 52
... whole disc has the same velocity as that of C and in the same direction . The motion is therefore a translation . OBS . In the general case why is not Q.AC the velocity of translation of the disc , and consequently . AC + w . CM the ...
... whole disc has the same velocity as that of C and in the same direction . The motion is therefore a translation . OBS . In the general case why is not Q.AC the velocity of translation of the disc , and consequently . AC + w . CM the ...
Page 55
... whole descends under the uniform accelerating force g like a solid mass . The comparison of these results is intended to elucidate the remark in ( 119 ) . 8. Let C ( fig . 20 ) be the centre of the wheel moving along the straight line ...
... whole descends under the uniform accelerating force g like a solid mass . The comparison of these results is intended to elucidate the remark in ( 119 ) . 8. Let C ( fig . 20 ) be the centre of the wheel moving along the straight line ...
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Common terms and phrases
2g h accelerating force Algebra angle angular velocity ball blow c² a² CA² Calculus Cambridge centre of gravity co-ordinate axes cone Conic Sections cos² cube cylinder diameter Differential Differential Calculus direction cosines disc distance dt dt dt dy dx dt dy dt effective force Examples Geometry Hence horizontal action horizontal and vertical HYMERS DR impulse inertia instantaneous axis invariable plane length Let C fig Ma² mass Mk² moment of inertia moves Mr² oscillation P₁ P₂ parallel particle perpendicular plates point of contact position pressure principal axes principle R₁ radius reaction revolves rotation sin² sphere tan² Third Edition Treatise velocities of translation vis viva w₁ w₂ wheel WHEWELL DR аф ᏧᎾ
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