Vector and Scalars

Vector and Scalars PowerPoint PPT Presentation


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Scalars versus Vectors. Scalar: A quantity that has a magnitude but no direction.Vector: A quantity that has both a magnitude (displacement) and direction.Vectors can be represented graphically or algebraically.. . . . . . . . . Quick Conventions II. The Glencoe Physics book will define vectors b

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Vector and Scalars

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1. Vector and Scalars

2. Scalars versus Vectors Scalar: A quantity that has a magnitude but no direction. Vector: A quantity that has both a magnitude (displacement) and direction. Vectors can be represented graphically or algebraically.

3. Quick Conventions II The Glencoe Physics book will define vectors by color: Displacement (m) Velocity (m/s) Acceleration (m/s2) Force (N) Momentum/Impulse

4. Vector and Scalars

5. Scalars versus Vectors Scalar: A quantity that has a magnitude but no direction. Vector: A quantity that has both a magnitude (displacement) and direction. Vectors can be represented graphically or algebraically.

6. Representing Vectors Example: Displacement Graphically= actually drawing an arrow Algebraically = numerical value

7. Graphically Representing Vectors Magnitude Magnitude is drawn as an arrows length. Longer arrows, larger magnitude.

8. Direction Graphically direction is represented by an arrow (tip to tail). N, S, E, W: Cartesian Coordinate System. Direction can be broken down into two parts:

9. Adding vectors=tip to tail Say we have two vectors a and b. To add them: Reposition one of the vectors so that the tip of one touches the tail of the other. Make a new vector going from the tail of the open end to the point of the other end.

10. Graphically adding vectors

11. Adding multiple vectors

12. Subtracting vectors Say we have two vectors a and b. To subtract them (a-b): Redraw vector b so that it has the opposite direction. (flip the tip and tail) Add the vectors as normal.

13. Visually subtracting vectors

14. Vector Examples Remember all vectors need a magnitude and direction. Measure direction with a protractor.

15. Quick Conventions I Take a look at this vector: 30° N of E 60° E of N While both are correct always put the protractor on the horizontal axis (EW) and measure to the north or south.

16. Graph Vectors Practice Pg 77-78 Problems: 1-5, 12, 20, 22

17. Vector and Scalars

18. Algebraically Representing Vectors Magnitude magnitude is assigned a number value. The magnitude should still have a unit such as 15-m.

19. Direction Algebraically direction is represented with degrees. use the form x° N/S of E/W Protractor should be lined up on the horizon No radians (check your calculator)

20. Breaking Down Vectors If you have a vector you can break it down into an x and y component. This is useful for adding.

21. Using Trig for Direction Useful formulas for 90° vectors: a2 + b2 = c2 sin ? = a/c cos ? = b/c tan ? = a/b Remember: DEGREE’s FYI: For non 90° r2 = a2 + b2 +2abcos ?.

22. Using Trig for Direction TRIG PNEMONIC sin ? = o/h cos ? = a/h tan ? = o/a Remember: SOA CAH TOA

23. Basic math and vectors vector + or - vector = vector vector x vector = scalar vector / vector = not done vector + or - scalar = can’t do vector x or / scalar = vector

24. Vectors and scalars When multiplying or dividing a vector by a scalar you only need to know two things: Either multiply or divide the magnitude of the vector. If the scalar is a negative number, reverse the direction of the vector.

25. Multiplying Vectors Multiplying vectors together is also called the dot product Calculus III: a • b = ||a|| ||b|| cos (?). Why do we need to know this? Force is defined as mass x acceleration Mass is a scalar, accel is a vector. Force therefore is a vector. (needs direction) Energy is defined as Force x distance. Force is a vector and distance is a vector. Energy therefore is a scalar. (no direction)

26. Trig Practice Problems Worksheet Practicing Pythagoras Trigonometry Word Problems

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