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274 final - Law of Cosines If(draw in 2 Moment about a line...

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Law of Cosines: L L Cartesian vector form: i+j+k C solve unknown Moments: M=Fd M=R x F (about a point in 3D) Right hand rule for +or- Moment about a line: 1.) 2.) (steps 1 and 2 get the scalar component of the moment) 3.) (Mbc)(ebc)= Mbc in Cartesian vector form. Ebc= a unit vector e running from b to c. If: (draw in) Must find Fxy first to find fx and fy correctly. Center of gravity of particles (A,B,C): W=Wa+Wb+Wc W …….. (same for Mxy) replace x with y and z for those. Same for center of mass but replace the weight with mass. Find the centroid of a rod. (Make a table.) 3D moments: 3 Separate I, j, k and add/set to 0/ solve Table for areas of centroids. Steps for solving 3D equilibrium problems: Locate all points and write as A=(x,y,z) Write out forces at each point Sum moments aobut the point with the most forces S set I’s , j’s and k’s = to 0 and solve. In case of a line that is not in the x,y or z direction must do Tbd=Tbd(unitv(d-b) (for a force going from b to d) Trusses:
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