# MSU ME 221 - LECTURE NOTES (13 pages)

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## LECTURE NOTES

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## LECTURE NOTES

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Lecture Notes

Pages:
13
School:
Michigan State University
Course:
Me 221 - Statics
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ME 221 Statics LECTURE 9 Sections 3 1 3 3 ME 221 Lecture 9 1 Exam 1 Results Average Score Scores posted on Angel Solution to be posted on Angel today See syllabus for regrade policy Homework 4 Chapter 3 problems ME 221 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 26 Lecture 9 3 Chapter 3 Rigid Bodies Moments Consider rigid bodies rather than particles Necessary to properly model problems Moment of a force Problems ME 221 Lecture 9 4 Rigid Bodies The point of application of a force is very important in how the object responds F F We must represent true geometry in a FBD and apply forces where they act ME 221 Lecture 9 5 Transmissibility A force can be replaced by an equal magnitude force provided it has the same line of action and does not disturb equilibrium B A ME 221 Lecture 9 6 Moment A force acting at a distance is a moment M M d is the perpendicular distance from F s line of action to O A O d F Defn of moment M Fd Transmissibility tells us the moment is the same about O or A ME 221 Lecture 9 7 Vector Product Moment of Force Define vector cross product trig definition component definition cross product of base vectors Moment in terms of cross product Example problems ME 221 Lecture 9 8 Cross Product The cross product of two vectors results in a vector perpendicular to both AxB A B A B sin n B A B The right hand rule decides the direction of the vector n ME 221 A AxB BxA BxA AxB AxB Lecture 9 9 Base Vector Cross Product Base vector cross products give us a means for evaluating the cross product in components i i 0 j i k k i j i j k j j 0 k j i i k j j k i k k 0 Here is how to remember all of this ME 221 j j i k i k Lecture 9 10 General Component Cross Product Consider the cross product of two vectors A i A j A k B i B j B k x y z x y z Ax By k Ax Bz j Ay Bx k Ay Bz i Az Bx j AzBy i Or matrix determinate gives a convenient calculation ME 221 i j k A B Ax Bx Ay By Az Bz Lecture 9 11 i j

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