mech_3_statics

# mech_3_statics - Newton's laws of motion second law...

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S YSTEM E QUILIBRIUM (S TATICS ) Forces Vector spring friction Gravitation Newton's laws of motion Moment, M=rxF Axial force, shear force Bending moment, twisting moment Solid mechanics or strength of materials kinetics conservation of momentum second law third law& first law third law

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Moment z x y F r d e O α By definition, the magnitude of the moment of F about O is M = F d (1) But this effect is uniquely defined if we associate this magnitude with a direction ‘ e ’ which is perpendicular to the plane which contains both vector F & r in a sense given by the right-hand screw rule. Therefore the moment can be regarded as a vector with a magnitude | F | | d | = | F | | r | sin and in the direction of e . Therefore M 0 = | F | | r | ( sin ) e = | F | | d | e (2) Vector product of two vectors The vector product of two vectors A and B is B A AxB B A BxA A x B ( A B ) has a magnitude | A | | B | sin where is the angle between vector. The direction of A x B is given by the right hand screw rule at shown. Note that vector product is not commutative. i.e. B x A A x B in fact B x A = - A x B A x B , in Cartesian form, we have
() ( ) AB A iA jA k B iB jB k xy z xy k ×= + + × + + since i x j = k = - j x i j x k = i = - k x j k x i = j = - i x k i x i = j x j = k x k =0 hence, A B ABi j k AB j i ABj k ABk i j xy xz yx yz zx zy × + +

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## This note was uploaded on 05/10/2009 for the course MXXM 2XX9 taught by Professor Gxxy during the Spring '09 term at City University of Hong Kong.

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mech_3_statics - Newton's laws of motion second law...

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