Solutions of the Examples Appended to A Treatise on the Motion of a Rigid Body |
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Page 2
... Hence for such a strip Σ ( myx ) becomes . § С œ ( a − x ) 3 tan2 B S X = 11⁄2 √ ( a2 x = 2 ( a2 x − 2 a x2 + x3 ) tan2 B. - Secondly , the required summation will be completed by adding the values of the function for such strips as ...
... Hence for such a strip Σ ( myx ) becomes . § С œ ( a − x ) 3 tan2 B S X = 11⁄2 √ ( a2 x = 2 ( a2 x − 2 a x2 + x3 ) tan2 B. - Secondly , the required summation will be completed by adding the values of the function for such strips as ...
Page 10
... hence the moment of inertia about a diameter whose direction cosines relatively to these are l , m , n , is = M 5 M 5 { ( b2 + c2 ) l2 + ( a2 + c2 ) m2 + ( a2 + b2 ) n2 } , { a2 + b2 + c2 — a3 l2 — b2 m2 - c2 n2 } . - - Now if the ...
... hence the moment of inertia about a diameter whose direction cosines relatively to these are l , m , n , is = M 5 M 5 { ( b2 + c2 ) l2 + ( a2 + c2 ) m2 + ( a2 + b2 ) n2 } , { a2 + b2 + c2 — a3 l2 — b2 m2 - c2 n2 } . - - Now if the ...
Page 11
... Hence we must have in the former example } a2 = } } ( a2 + b2 ) + b2 , a2 = 662 , a = b√6 , a and b being the half axes of the solid . In the latter example if a be the altitude , c the radius of the cone's base , ( 4a2 + c2 ) , 3 = 10 ...
... Hence we must have in the former example } a2 = } } ( a2 + b2 ) + b2 , a2 = 662 , a = b√6 , a and b being the half axes of the solid . In the latter example if a be the altitude , c the radius of the cone's base , ( 4a2 + c2 ) , 3 = 10 ...
Page 15
... Hence if this force be applied in the reversed direction CO , there will be equilibrium between it , the weight , and the reaction of the axis . Since the two former forces are in the plane ABO , the latter reaction is in this plane ...
... Hence if this force be applied in the reversed direction CO , there will be equilibrium between it , the weight , and the reaction of the axis . Since the two former forces are in the plane ABO , the latter reaction is in this plane ...
Page 19
... Hence if * be the angle which the base makes with its original position , the distance of the centre of gravity of the body from the axis , d2 ( 102 +72 ) dt ( 162 + ñ3 ) ( do ) dt 2 = = - gr sin a . coso , 2gr sin a . sin ; therefore ...
... Hence if * be the angle which the base makes with its original position , the distance of the centre of gravity of the body from the axis , d2 ( 102 +72 ) dt ( 162 + ñ3 ) ( do ) dt 2 = = - gr sin a . coso , 2gr sin a . sin ; therefore ...
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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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