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BASIC VECTOR NOTES

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Introduction to vector, for Malaysian Polytechnic's students.
Especially for IT courses

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BASIC VECTOR NOTES

  1. 1. 1
  2. 2. 2 Understand vector quantities • State the two components of a vector. • Draw a directed line to represent a vector.
  3. 3.  Quantities such as time, temperature and mass are entirely defined by a numerical value and are called scalars or scalar quantities. › E.g. temperature in a room is 16 C.  Quantities such as velocity, force and acceleration, which have both a magnitude and a direction, are called vectors. › E.g. the velocity of a car is 90km/h due west. 3
  4. 4.  4
  5. 5.  A vector quantity can be represented graphically by a line, drawn so that: › the length of the line denotes the magnitude of the quantity, and › the direction of the line denotes the direction in which the vector quantity acts.  An arrow is used to denote the sense, or direction, of the vector.  The arrow end of a vector is called the ‘nose’ and the other end the ‘tail’. 5
  6. 6.  For example, a force of 9N acting at 45◦ to the horizontal is shown in Fig. 1. Note that an angle of +45◦ is drawn from the horizontal and moves anticlockwise. Fig. 1 6
  7. 7.  A velocity of 20m/s at −60◦ is shown in Fig. 2. Note that an angle of −60◦ is drawn from the horizontal and moves clockwise. Fig. 2 7
  8. 8.  8
  9. 9. 9 Solve addition vectors: • Determine the resultant vector using graphical method: i) triangle method, ii) parallelogram method.
  10. 10.  Adding two or more vectors by drawing assumes that a ruler, pencil and protractor are available.  Results obtained by drawing are naturally not as accurate as those obtained by calculation. 10
  11. 11.  Triangle @ Nose-to-tail method › Two force vectors, F1 and F2, are shown in Fig. 3. › When an object is subjected to more than one force, the resultant of the forces is found by the addition of vectors. Fig. 3 11
  12. 12.  To add forces F1 and F2: › Force F1 is drawn to scale horizontally, shown as Oa in Fig. 4. › From the nose of F1, force F2 is drawn at angle θ to the horizontal, shown as ab. › The resultant force is given by length Ob, which may be measured.  This procedure is called the ‘nose-to-tail’ or ‘triangle’ method. 12
  13. 13. a b 0 Fig. 4 Fig. 3 13
  14. 14.  Parallelogram method › To add the two force vectors, F1 and F2, of Fig. 3: › A line cb is constructed which is parallel to and equal in length to Oa (see Fig. 5). › A line ab is constructed which is parallel to and equal in length to Oc. › The resultant force is given by the diagonal of the parallelogram, i.e. length Ob.  This procedure is called the ‘parallelogram’ method. 14
  15. 15. a b 0 Fig. 5 Fig. 3 c 15
  16. 16.  A force of 5N is inclined at an angle of 45◦ to a second force of 8 N, both forces acting at a point. Find the magnitude of the resultant of these two forces and the direction of the resultant with respect to the 8N force by: › (a) the ‘nose-to-tail’method, and › (b) the ‘parallelogram’ method. Answer: 12N at (approximately) 17˚ from horizontal 16
  17. 17. Answer: 18N at (approximately) 34˚ from horizontal 17
  18. 18. Answer: 22m/s at (approximately) 105˚ from horizontal 18
  19. 19. 19
  20. 20. Prepare for Quiz 1 and Peer Assessment 1, for next class! 20

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