Moment of a Force About a Point.A force vector is defined by its magnitude anddirection. Its effect on the rigid body also dependsMoon its point of application.: The moment of F about O is defined asMo=rxF: The moment vector Mo is perpendicular to theplane containing O and the force F.(a): Magnitude of Mo measures the tendency of the forceto cause rotation of the body about an axis along MoMoMo =rFsin0=FdThe sense of the moment may be determined by theright-hand rule(b):Anyforce F'that has the same magnitude anddirection as F, is equivalent if it also has the same lineof action and therefore,produces the same moment6
Moment of a Force About a Point • A force vector is defined by its magnitude and direction. Its effect on the rigid body also depends on its point of application. • The moment of F about O is defined as MO r F • The moment vector MO is perpendicular to the plane containing O and the force F. • Any force F’ that has the same magnitude and direction as F, is equivalent if it also has the same line of action and therefore, produces the same moment. • Magnitude of MO measures the tendency of the force to cause rotation of the body about an axis along MO . The sense of the moment may be determined by the right-hand rule. MO rF sin Fd 6
Sample ProblemA 100-lb vertical force is applied to the end of aleverwhichisattachedtoashaftatODetermine:24 in.a) moment about O,1001bb) horizontal force at A which creates the samemoment,60°c) smallest force at A which produces the samemoment,d) location for a 240-lb vertical force to producethe same moment,)whetheranyoftheforcesfromb,c,anddisequivalenttotheoriginalforce.7
Sample Problem A 100-lb vertical force is applied to the end of a lever which is attached to a shaft at O. Determine: a) moment about O, b) horizontal force at A which creates the same moment, c) smallest force at A which produces the same moment, d) location for a 240-lb vertical force to produce the same moment, e) whether any of the forces from b, c, and d is equivalent to the original force. 7
a) Moment about O is equal to the product of theforce and the perpendicular distance between theline of action of theforce and O.Since the forcetendstorotatetheleverclockwise.themoment24 in1001hvectoris intotheplaneofthepaper.Mo = Fd60°d =(24in.)cos60°=12 inMMo = (100 1b)(12 in.)Mo =12001b·in8
a) Moment about O is equal to the product of the force and the perpendicular distance between the line of action of the force and O. Since the force tends to rotate the lever clockwise, the moment vector is into the plane of the paper. 100 lb12 in. 24in. cos60 12 in. O O M d M Fd MO 1200 lbin 8