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Introduction to Vectors. Vectors ScalarsVectors Distance Time Mass Work Energy Speed Displacement Velocity Acceleration Force Momentum Torque Magnitude.

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Presentation on theme: "Introduction to Vectors. Vectors ScalarsVectors Distance Time Mass Work Energy Speed Displacement Velocity Acceleration Force Momentum Torque Magnitude."— Presentation transcript:

1 Introduction to Vectors

2 Vectors ScalarsVectors Distance Time Mass Work Energy Speed Displacement Velocity Acceleration Force Momentum Torque Magnitude Only Magnitude and Direction

3 Vectors have magnitude and direction, but no place Vectors

4 Two vectors are equal if they have the same magnitude and the same direction

5 Vectors Scaling Vectors

6 Vectors Scaling a Displacement Vector

7 Vectors Scaling a Change in Velocity Vector

8 Vectors Vector Addition (Graphical)

9 Vectors Vector Subtraction (Graphical)

10 Vectors Vector Subtraction (Graphical)

11 Vectors Vector Subtraction (Graphical)

12 The Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors that make a right angle to each other.

13 x y The parallelogram method of vector resolution involves using an accurately drawn, scaled vector diagram to determine the components of the vector.

14 x y The trigonometric method of vector resolution involves using trigonometric functions to determine the components of the vector.

15 Vectors x y Vector Components

16 A B R AxAx BxBx RxRx AyAy ByBy RyRy x y Adding Vectors using Vector Components

17 A B R AxAx BxBx RxRx AyAy ByBy RyRy x y

18 Vectors F2F2 22 F3F3 33 F4F4 44 F1F1 11

19 F1F1 F2F2 F3F3 F4F4 11 22 33 44 F 1 = 50 N  1 = 30 o F 2 = 100 N  2 = 135 o F 3 = 30 N  3 = 250 o F 4 = 40 N  4 = 300 o   10.3   34.6  Adding Vectors using Vector Components

20 Vectors F R = 37.4 N RR  

21 Vectors F1F1 F2F2 F3F3 F4F4 11 22 33 44 F 1 = 90 N  1 = 45 o F 2 = 80 N  2 = 150 o F 3 =50 N  3 = 220 o F 4 = 70 N  4 = 340 o 63.6  69.3   23.9  F R = 52.4 N RR

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