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lctr13_s12

# lctr13_s12 - 4.1Momentofaforce Themomentofaforce(M...

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§ 4.1  Moment of a force The  moment of a force  ( M ”  r × F ) is a measure of the  tendency of the force to produce  rotation  of a body about a  point or axis.  The proof of this is reserved for Dynamics,  where we represent a body as an  assembly  of particles,  each particle governed by Newton’s Second Law.  By  taking the cross-product of a suitable relative position  vector into each of these particle equations of motion, and  summing over all particles, we can show that a body’s  rotational dynamics  are governed by equations like: α I M G G =

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Dynamic Motion in 3D In 3D, a single rigid body has three translational dynamics equations… …accompanied by three rotational dynamics equations: Gz z Gy y Gx x ma F ma F ma F = = = z Gz Gz y Gy Gy x Gx Gx I M I M I M α = = = In 3D, a stationary rigid body must be in both translational and rotational equilibrium.   Setting all linear and angular accelerations to zero, we have: 0 0 0 = = = z y x F F F 0 0 0 = = = Gz Gy Gx M M M
Moments of Forces The moment of a force M  ”   r  ×  F is perpendicular to the plane defined by the relative

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lctr13_s12 - 4.1Momentofaforce Themomentofaforce(M...

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