Solutions of the Examples Appended to A Treatise on the Motion of a Rigid Body |
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Page 12
... angular velocity d Ꮎ dt dt d Ꮎ = a sec2 0 ; = = 1 - α · cos2 0 , 1 2 a ( 1 + cos 20 ) . C + 1 ( 0+ sin 20 ) . .. t = C + 2 a 2 therefore if the integral be taken between values of sepa- rated by the interval 2π , we have 2π time of ...
... angular velocity d Ꮎ dt dt d Ꮎ = a sec2 0 ; = = 1 - α · cos2 0 , 1 2 a ( 1 + cos 20 ) . C + 1 ( 0+ sin 20 ) . .. t = C + 2 a 2 therefore if the integral be taken between values of sepa- rated by the interval 2π , we have 2π time of ...
Page 15
... angular velocity of the body , the effective force on a particle of mass m at distance r from the axis is mor towards the axis , and the resultant of such is M. CO in OC . Hence if this force be applied in the reversed direction CO ...
... angular velocity of the body , the effective force on a particle of mass m at distance r from the axis is mor towards the axis , and the resultant of such is M. CO in OC . Hence if this force be applied in the reversed direction CO ...
Page 19
... angular velocity in the lowest position when = π 2 w2 2gr sin a ka2 + 72 In the same position , the resultant effective force is Mw2r towards the axis , = 272 Mg sin a , k + 2. ( 8 ) 2 Mg sin a , = - 45 Mg sin a . Hence the pressure on ...
... angular velocity in the lowest position when = π 2 w2 2gr sin a ka2 + 72 In the same position , the resultant effective force is Mw2r towards the axis , = 272 Mg sin a , k + 2. ( 8 ) 2 Mg sin a , = - 45 Mg sin a . Hence the pressure on ...
Page 20
... angular velocity in its lowest position , the pressure on the axis in that position == Mg + Mw2 α This pressure will therefore be least when has the least value compatible with the condition of the body making com- plete revolutions ...
... angular velocity in its lowest position , the pressure on the axis in that position == Mg + Mw2 α This pressure will therefore be least when has the least value compatible with the condition of the body making com- plete revolutions ...
Page 24
... angular velocity w , and be suddenly fixed at B and thus brought to rest in a horizontal position . Let be the distance from A of a mole- cule m . Such a molecule is moving before the check with the velocity wr , and therefore the ...
... angular velocity w , and be suddenly fixed at B and thus brought to rest in a horizontal position . Let be the distance from A of a mole- cule m . Such a molecule is moving before the check with the velocity wr , and therefore the ...
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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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