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Mechanics

Mechanics. AP200 Dr. C. W. Ong Meriam, J.L., Kraige, L.G., “Engineering Mechanics, Dynamics”, John Wiley Course Work 30% (Exercises and tests) Examination 70% Download materials http://ap.polyu.edu.hk/apacwong/. A. Chapter 1 Vector.

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Mechanics

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  1. Mechanics AP200 Dr. C. W. Ong Meriam, J.L., Kraige, L.G., “Engineering Mechanics, Dynamics”, John Wiley Course Work 30% (Exercises and tests) Examination 70% Download materials http://ap.polyu.edu.hk/apacwong/

  2. A Chapter 1 Vector A vector has a length A and a direction (unit vector)

  3. y  x 2D Cartesian coordinate system(one form of presentation) Pythagoras theorem

  4. z Az y Ax Ay x 3-D Cartesian coordinate system

  5. y y x x O Addition of vectors Subtraction of vectors O

  6. y x Dot (scalar) product of two vectors Definition: Note: AB cos = AB cos (A - B) = AB(cos A cos B +sin A sin B) = (Acos A)(Bcos B) + (Asin A) (Bsin B) In 2-D Cartesian coordination system

  7. y  O In 3-D Cartesian coordinate system: x From cosine law:

  8. l A A’ a  Application of dot product: Projection Area = l a Projected area = = l a cos 

  9. 30o 60o Exercise: Find the projection of vector with a length of 10 unit along .

  10. k j i Cross product

  11. y x

  12. In Cartesian coordinatesystem:

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