Solutions of the Examples Appended to A Treatise on the Motion of a Rigid Body |
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Page 5
... diameters of the circle ( 9 ) , and these latter are equal to one another , therefore either of them = Mr2 . A homo- 5. Let a , ẞ be the semi - axes of one stratum . geneous spheroid bounded by this surface will have about its axis of ...
... diameters of the circle ( 9 ) , and these latter are equal to one another , therefore either of them = Mr2 . A homo- 5. Let a , ẞ be the semi - axes of one stratum . geneous spheroid bounded by this surface will have about its axis of ...
Page 10
... diameter inclined at an angle a to the major axis is M { b2 cos2 a + a sina } . ( 21 ) 14 . 1 cos a sin2 a Now = + ... diameter whose direction cosines relatively to these are l , m , n , is = M 5 M 5 { ( b2 + c2 ) l2 + ( a2 + c2 ) m2 + ...
... diameter inclined at an angle a to the major axis is M { b2 cos2 a + a sina } . ( 21 ) 14 . 1 cos a sin2 a Now = + ... diameter whose direction cosines relatively to these are l , m , n , is = M 5 M 5 { ( b2 + c2 ) l2 + ( a2 + c2 ) m2 + ...
Page 14
... diameter of its base is 2 π 3 3 4 = . 15 π , the density being 1 ; therefore if dr be the thickness of an indefinitely thin shell , its moment of inertia is πrt.dr. Again , the moment of the solid hemisphere about its base is 2π 7.3 · 3 ...
... diameter of its base is 2 π 3 3 4 = . 15 π , the density being 1 ; therefore if dr be the thickness of an indefinitely thin shell , its moment of inertia is πrt.dr. Again , the moment of the solid hemisphere about its base is 2π 7.3 · 3 ...
Page 20
... diameter of the spheroid's equa- tor . If a , c be the semi - axes of the spheroid , the axis a2 + c2 5 required is at a distance √2 diameter of the equator . - g from a parallel 11. Let a be the length of an edge of the cube . If w be ...
... diameter of the spheroid's equa- tor . If a , c be the semi - axes of the spheroid , the axis a2 + c2 5 required is at a distance √2 diameter of the equator . - g from a parallel 11. Let a be the length of an edge of the cube . If w be ...
Page 26
... diameter perpendicular to the tangent line . The effective force has a resultant acting through some point in this line perpendicular to the plane , by reason of the symmetry of the figure and its motion about AB . If then the blow be ...
... diameter perpendicular to the tangent line . The effective force has a resultant acting through some point in this line perpendicular to the plane , by reason of the symmetry of the figure and its motion about AB . If then the blow be ...
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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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