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Notes: Vectors

Notes: Vectors. Scalar – a quantity that has magnitude (how much) ex. distance, time, mass, volume, speed Vector – a quantity that has magnitude and direction . (how much, which way) ex. displacement, velocity →

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Notes: Vectors

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  1. Notes: Vectors Scalar – a quantity that has magnitude (how much) ex. distance, time, mass, volume, speed Vector – a quantity that has magnitude and direction. (how much, which way) ex. displacement, velocity → A - symbol for a vector Represented as a line segment with an arrow-tip.

  2. Notes: Vectors Direction can be represented in 3 various ways: • by sign: -20Newtons (down) • by actual direction: +20 m/s (North) 3. as a graphical line segment with an arrow-tip.

  3. http://phet.colorado.edu/sims/vector-addition/vector-addition_en.htmlhttp://phet.colorado.edu/sims/vector-addition/vector-addition_en.html II. Vector Addition • Resultant – representation of net sum of all vectors → (R) B. When collinear vectors are added, in the same linear plane, the resultant is the sum of all the vectors. Vectors may be added in any order, graphically or mathematically, to obtain the same resultant. Vectors may be moved parallel to their original position. C. When vectors are added at an angle, The Graphic, Tip-to-tail, Parallelogram, or Trig Method needs to be used

  4. II. Vector Addition When collinear vectors are added, in the same linear plane, the resultant is the sum of all the vectors. Horizontally Vertically

  5. II. Vector Addition Collinear vectors may be added algebraically. Vectors may be added in any order to obtain the same resultant. (ex: Displacement)

  6. II. Vector Addition Collinear vectors may be added graphically (Displacement) • Must measure resultant using a ruler on a graph

  7. II. Vector additionNon-linear vectors may be added mathematicallyusing Pythagorean Theorem(ex: Displacement) CANNOT SIMPLY ADD VALUES OF VECTORS!

  8. II. Vector additionNon-linear vectors may be added graphicallyusing Pythagorean Theorem(ex: Displacement) CANNOT SIMPLY ADD VALUES OF VECTORS!

  9. II. Vector AdditionFinding Magnitude and Displacement of Resultant If two vectors are at right angles, or 90°, may use Pythagorean Theorem a2 + b2 = c2 x2 + y2 = R2 If two vectors are at an angle other than 90°, may use Law of Cosines a2 + b2 - 2abcosθ = R2 Use tangent to find direction for vectors at 90° tan θ = opp/adj

  10. II. Vector Addition

  11. II. Vector Addition Non-linear vectors may be added graphically using tip-to-tail method (ex: Displacement) • Must measure resultant using a ruler on a graph

  12. C.1. Steps for Tip-to-tail Method a. Set up an equality scale. ex: 1cm = 1 km b. Convert magnitudes of measurements to lengths of vector arrows. c. Select an origin or starting point. d. Draw the first vector from the starting point. e. Draw the second vector starting from the tip of the first vector. f. Draw the resultant from the original start point to the tip of the last vector. g. Measure the length of the resultant and angle. h. Convert the length of the resultant arrow back to the magnitude.

  13. Tip-to-Tail Method 3 2 1

  14. II. Vector Addition Non-linear vectors may be added mathematically (ex: Displacement)

  15. Tip-to-Tail Method Vectors may be added in any order, graphically or mathematically, to obtain the same resultant. Vectors may be moved parallel to their original position.

  16. Graphic/Tip to tail Method (Rocket and Wind)

  17. Parallelogram Method

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