PowerPoint PresentationExam #1 ResultsHomework #4Chapter 3 Rigid Bodies; MomentsRigid BodiesTransmissibilityMomentVector Product; Moment of ForceCross ProductBase Vector Cross ProductGeneral Component Cross ProductSlide 12Slide 13ME 221 Lecture 9 1ME 221 StaticsLECTURE #9Sections: 3.1 - 3.3Exam #1 ResultsAverage Score: ?Scores posted on AngelSolution to be posted on Angel todaySee syllabus for regrade policyME 221 Lecture 9 3Homework #4•Chapter 3 problems:–1, 4, 8, 11, 17, 25, 26, 28, 35 & 40–To be solved using hand calculations–May check work using MathCAD, Matlab, etc.–Due Friday, September 26ME 221 Lecture 9 4Chapter 3Rigid Bodies; Moments•Consider rigid bodies rather than particles–Necessary to properly model problems•Moment of a force•ProblemsME 221 Lecture 9 5Rigid Bodies•The point of application of a force is very important in how the object respondsFF•We must represent true geometry in a FBD and apply forces where they act.ME 221 Lecture 9 6Transmissibility•A force can be replaced by an equal magnitude force provided it has the same line of action and does not disturb equilibriumBAME 221 Lecture 9 7Moment•A force acting at a distance is a moment•Transmissibility tells us the moment is the same about O or AFdMOMAd is the perpendiculardistance from F’s lineof action to ODefn. of moment: M = FdME 221 Lecture 9 8Vector Product; Moment of Force•Define vector cross product–trig definition–component definition•cross product of base vectors•Moment in terms of cross product•Example problemsME 221 Lecture 9 9Cross ProductThe cross product of two vectors results in a vector perpendicular to both.ˆsin A B A B nBAA x BThe right-hand rule decides the direction of the vector.B x AABA x B = - B x An =AxBAxB^ME 221 Lecture 9 10Base Vector Cross ProductBase vector cross products give us a means for evaluating the cross product in components.ˆ ˆ ˆ ˆ ˆ ˆˆ ˆ; ;ˆ ˆ ˆ ˆ ˆ ˆˆ ˆ; ;ˆ ˆ ˆ ˆˆ ˆ ˆ ˆ; ;               i i 0 j i k k i ji j k j j 0 k j ii k j j k i k k 0Here is how to remember all of this:ˆiˆjˆk+ˆiˆk-ˆjME 221 Lecture 9 11General Component Cross ProductConsider the cross product of two vectors   ˆ ˆ ˆ ˆˆ ˆx y z x y zA A A B B B    i j k i j kˆx yA B kˆx zA B jˆy xA B kˆy zA B iˆz xA B jˆ AzBy iOr, matrix determinate gives a convenient calculationˆ ˆˆx y zx y zA A AB B B i j kA BME 221 Lecture 9 12ˆ ˆˆx y zx y zA A AB B B i j kA Bˆ ˆˆx y zx y zA A AB B B i j kA B -ˆ ˆˆx y zx y zA A AB B B i j kA B +=(AyBz-AzBy) i- (AxBz-AzBx) j+ (AxBy-AyBx)kME 221 Lecture 9 13ProblemsA = 5i + 3jB = 3i + 6jFind•A·B•The angle between A and