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Vectors and Scalars <ul><li>Scalar – a measurement that indicates an amount without specifying direction  </li></ul><ul><l...
Where do we see vectors in physics? <ul><li>Motion – distance and displacement; speed and velocity </li></ul><ul><ul><li>M...
Distance and Displacement North 20 km East 15 km South 8 km West 20 km Find the distance traveled = ____ Find the displace...
 
 
 
Option 1 – protractor (not bad)
Option 2 – Trig (more accurate) θ Heading (bearing) is ____ –  θ  = _______
Speed and Velocity South 32 km East 24 km Time = 2.5 hours North 9 km West 45 km Find the speed = ____ Find the velocity =...
θ Heading is _____ +  θ  = ________
Difference between quantities <ul><li>Scalar Quantities (distance, speed) </li></ul><ul><ul><li>Indicate size only (metres...
Try these – draw and calculate <ul><li>Walk 25 m [N], then 15 m [W], then 10 m [N], then 5 m [E], finally 15 m [S]  </li><...
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Vectors and Scalars

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Intro to vectors and scalars for SPH3U1

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Vectors and Scalars

  1. 1. Vectors and Scalars <ul><li>Scalar – a measurement that indicates an amount without specifying direction </li></ul><ul><li>Vector – a measurement that indicates both an amount and a direction </li></ul><ul><li>Why is this important? </li></ul><ul><ul><li>Physics requires precision </li></ul></ul><ul><ul><li>Distinction between the actual path of an object and the shortest path from A to B </li></ul></ul>
  2. 2. Where do we see vectors in physics? <ul><li>Motion – distance and displacement; speed and velocity </li></ul><ul><ul><li>Motion at constant speed (changing directions) </li></ul></ul><ul><ul><li>Motion in two dimensions </li></ul></ul><ul><ul><ul><li>With or against a current or wind </li></ul></ul></ul><ul><ul><ul><li>With or against gravity </li></ul></ul></ul><ul><li>Forces – direction of a force applied to an object </li></ul><ul><ul><li>Objects speed up or slow down in the direction of the net force </li></ul></ul>
  3. 3. Distance and Displacement North 20 km East 15 km South 8 km West 20 km Find the distance traveled = ____ Find the displacement = ___ at ___ O
  4. 7. Option 1 – protractor (not bad)
  5. 8. Option 2 – Trig (more accurate) θ Heading (bearing) is ____ – θ = _______
  6. 9. Speed and Velocity South 32 km East 24 km Time = 2.5 hours North 9 km West 45 km Find the speed = ____ Find the velocity = ___ at ___ O
  7. 10. θ Heading is _____ + θ = ________
  8. 11. Difference between quantities <ul><li>Scalar Quantities (distance, speed) </li></ul><ul><ul><li>Indicate size only (metres, km/hr, etc) </li></ul></ul><ul><ul><li>Measure the entire path – start to finish </li></ul></ul><ul><li>Vector Quantities (displacement, velocity) </li></ul><ul><ul><li>Indicate both size and direction (km/hr [W]) </li></ul></ul><ul><ul><li>Measure the shortest distance between the starting and ending points = “as the crow flies” </li></ul></ul><ul><li>Calculating Angles – unless the resulting angle is directly N, S, E, or W, you will </li></ul><ul><ul><li>Use trig to determine the angle from start to finish </li></ul></ul><ul><ul><li>Convert that angle into a bearing between 0 and 360 degrees (0 = North, 180 = South, etc) </li></ul></ul>
  9. 12. Try these – draw and calculate <ul><li>Walk 25 m [N], then 15 m [W], then 10 m [N], then 5 m [E], finally 15 m [S] </li></ul><ul><ul><li>Find both distance AND displacement </li></ul></ul><ul><li>Drive 60 km [S], then 5 km [W], then 20 km [S], then 25 km [E], then 5 km [N] in 85 minutes </li></ul><ul><li>Find both the speed and the velocity (be sure to include the heading) </li></ul>

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