Vectors

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Vectors

  1. 1. Vectors Notes
  2. 2. VELOCITY VECTORS <ul><li>VECTOR: An arrow drawn to scale that represents the magnitude and direction of a given velocity. </li></ul>10m/s left 5m/s rt
  3. 3. Scaled Vector Diagrams <ul><li>There are several characteristics of this diagram which make it an appropriately drawn vector diagram. </li></ul><ul><ul><li>a scale is clearly listed </li></ul></ul><ul><ul><li>a vector arrow (with arrowhead) is drawn in a specified direction. The vector arrow has a head and a tail . </li></ul></ul><ul><ul><li>the magnitude and direction of the vector is clearly labeled. </li></ul></ul>
  4. 4. Direction Conventions <ul><li>Use East as zero degrees. </li></ul><ul><li>Click here to practice: </li></ul>Practice set at The Physics Classroom
  5. 5. <ul><li>RESULTANT: The single vector that results when two vectors are combined. </li></ul>10m/s left 5m/s rt 5m/s left
  6. 6. Turn to the question on Page 17: <ul><li>A motor boat is moving 10 km/h relative to the water. If the boat travels in a river that flows at 10km/h, what is the velocity relative to the shore when it heads directly up stream? </li></ul><ul><li>When it heads directly downstream? </li></ul>
  7. 7. Adding Noncollinear vectors <ul><li>The Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors which make a right angle to each other. </li></ul>
  8. 8. Graphical Vector Addition: A + B <ul><li>Step 1- Draw a start point. </li></ul><ul><li>Step 2- Decide on a scale. </li></ul><ul><li>Step 3- Draw Vector A to scale. </li></ul><ul><li>Step 4- Vector B’s tail begins at Vector A’s head. Draw Vector B to scale. </li></ul><ul><li>Step 5- Draw a line connecting the initial start point to the head of B. This is the resultant. </li></ul><ul><li>Step 6- Measure the resultant’s length with a ruler and direction with a protractor. </li></ul><ul><li>Step 7- Convert back to the given units using your scale. </li></ul>
  9. 9. Animation of head-to-tail vector addition – three times
  10. 10. Practice Graphical Addition Practice Set at The Physics Classroom
  11. 11. Resultants and Equilibrants <ul><li>The resultant is the vector sum of two or more vectors. It is the result of adding two or more vectors together. </li></ul><ul><li>The equilibrant is the balancing vector… the vector equal in magnitude but opposite in direction to the resultant. </li></ul>
  12. 12. Vector Components <ul><li>Some vectors are directed at angles to the coordinate axes, and will need to be transformed into two parts with each part being directed along the axes. Each part of a two-dimensional vector is known as a component . </li></ul><ul><li>Any vector directed in two dimensions can be thought of as having an influence in two different directions. The components of a vector depict the influence of that vector in a given direction. </li></ul>

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