Solutions of the Examples Appended to A Treatise on the Motion of a Rigid Body |
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Page 21
... acting towards AD , and if such forces be reversed , the moment of their resultant about A when the rod AB is considered = Σ ( mr2 cot a ) w3 , = cot a sin2 a.wx moment of inertia of AB about a per- pendicular axis at A , AB2 = M. · w2 ...
... acting towards AD , and if such forces be reversed , the moment of their resultant about A when the rod AB is considered = Σ ( mr2 cot a ) w3 , = cot a sin2 a.wx moment of inertia of AB about a per- pendicular axis at A , AB2 = M. · w2 ...
Page 24
... acting downwards , and if this be applied upwards the re- sultant of such reversed forces , together with R the initial reaction at the fixed point , can balance the weight Mg of the rod . .. Mg = R + Σ ( mr ) . ga a2 + k2 ' a2 = R + Mg ...
... acting downwards , and if this be applied upwards the re- sultant of such reversed forces , together with R the initial reaction at the fixed point , can balance the weight Mg of the rod . .. Mg = R + Σ ( mr ) . ga a2 + k2 ' a2 = R + Mg ...
Page 25
... acting in a reversed direction , i.e. opposite to P , can maintain equilibrium with P and the reaction of the axis . Hence the latter reaction is perpendicular to the plane , and may be exhibited by two impulsive forces R , R ' at A and ...
... acting in a reversed direction , i.e. opposite to P , can maintain equilibrium with P and the reaction of the axis . Hence the latter reaction is perpendicular to the plane , and may be exhibited by two impulsive forces R , R ' at A and ...
Page 26
... 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 applied at a point not in AB , this impulse will have an unbalanced moment about ...
... 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 applied at a point not in AB , this impulse will have an unbalanced moment about ...
Page 44
... acting upon it form a couple consisting of the given impulse and an equal contrary impulse at the centre of gravity . The cube is a body for which the central ellipsoid is a sphere . Hence the initial instantaneous axis is perpendicular ...
... acting upon it form a couple consisting of the given impulse and an equal contrary impulse at the centre of gravity . The cube is a body for which the central ellipsoid is a sphere . Hence the initial instantaneous axis is perpendicular ...
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2g h accelerating force Algebra angle angular velocity ball blow cČ aČ CAČ Calculus Cambridge centre of gravity co-ordinate axes cone Conic Sections cosČ 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 MaČ mass MkČ moment of inertia moves MrČ oscillation P₁ P₂ parallel particle perpendicular plates point of contact position pressure principal axes principle R₁ radius reaction revolves rotation sinČ sphere tanČ Third Edition Treatise velocities of translation vis viva w₁ w₂ wheel WHEWELL DR аф ᏧᎾ
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