Analytical mechanics for students of physics and engineering . 16. Supposing the weights of the following figures to be in equilibriumfind their relative magnitudes. The circles which are tangent to othercircles represent 54. Resultant of a System of Forces Acting upon a Rigid Body.—We have already the most general displacementof a rigid body consists of a translation along, and a rotationabout, a certain lino. Therefore such a displacement can beprevented by a single force opposed to the translation andasingle torque opposed to the rotation. Thus a Bingle forceand a single
Analytical mechanics for students of physics and engineering . 16. Supposing the weights of the following figures to be in equilibriumfind their relative magnitudes. The circles which are tangent to othercircles represent 54. Resultant of a System of Forces Acting upon a Rigid Body.—We have already the most general displacementof a rigid body consists of a translation along, and a rotationabout, a certain lino. Therefore such a displacement can beprevented by a single force opposed to the translation andasingle torque opposed to the rotation. Thus a Bingle forceand a single torque can be found which will keep a rigid bodyin equilibrium against the action of any system of forces. 48 ANALYTICAL MECHANICS The resultant of a system of forces consists, therefore, of asingle force and a single torque which, when reversed, willkeep the rigid body in equilibrium against the action of thegiven system of forces. 55. Resultant of Coplanar Forces Acting upon a Rigid Body. —Let Fi, F>, . . Fn denote the given forces and let the xy-plane be their plane of action. Then, if R, X, and Y denotethe resultant force and its components, respectively, we have X = Xi + X2+ • ? • + xn, Y = Fi+IV+ . .
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