Moment of a Force Moment of force denotes the tendency of that force to cause rotation about a specific axis/point. Also known as torque. Notation : Moment about point O about the z axis denoted by (MO)z. Rotation is caused only if the line of action of the force does not pass through the point O. Rotation about Different Axes For a given point O, rotation can be about any axis. Applying force in the xdirection causes rotation about zaxis. Applying force in the ydirection causes no rotation. Magnitude of Moment Magnitude is not only function of the force applying the moment, but the distance from the point O. Example: Loosening bolt, opening door. MO = Fd, where d is the perpendicular distance from O to the line of action of F. Units are force·distance (N·m, lb·ft). Direction of Moment Direction is determined by righthand rule. Curl fingers in direction of rotation, thumb points along moment. Direction is only convention. Resultant Moment For coplanar systems (all points, vectors on same plane), only 2 options for direction, up or down. Therefore in these systems, all moments can be expressed as either positive or negative. Convention is that counterclockwise is positive. Resultant moment can therefore be found using scalar equation: MRo = Σ Fd Concept The direction of the B moment caused by the force F at A,B,C will be: A a) Out, in, out F b) In, in, out c) Out, out, in d) In, out, in C Cross Product Defined as A x B = AB sin uc, where uc is a vector perpendicular to both A and B. uc is found using the righthand rule. o o Note that sin 0 = 0, sin 90 = 1 (maximum). Cross product of 2 parallel vectors is zero, while it is maximised for perpendicular vectors. Magnitude is equal to area of parallelogram formed by the 2 vectors. Also known as vector product. Cartesian Cross Product Note that i x i = 0, etc. The cross product of 2 unit vectors gives the remaining unit vector (could be negative).
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