Introduction to Vectors. Vectors ScalarsVectors Distance Time Mass Work Energy Speed Displacement...

Introductionto Vectors

Vectors

Scalars Vectors

Distance

Energy

Displacement

Velocity

Acceleration

Momentum

Torque

MagnitudeOnly

Magnitudeand

Direction

Vectors have magnitude and direction,but no place

Vectors

Two vectors are equal if they have the same magnitude

and the same direction

Vectors

Scaling Vectors

Vectors

Scaling a Displacement Vector

Vectors

Scaling a Change in Velocity Vector

Vectors

Vector Addition (Graphical)

Vectors

Vector Subtraction (Graphical)

Vectors

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.

yA yx AAA

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

cosAAx

sinAAy

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

Vectors

2x AAA

Vector Components

2x RRR

xxx BAR

yyy BAR

Adding Vectors using Vector Components

2x RRR

xxx BAR

yyy BAR

βcosBB

αcosAA

βsinBB

αsinAA

Vectors

knR FF

FFFFF R

F1 = 50 N 1 = 30o

F2 = 100 N 2 = 135o

F3 = 30 N 3 = 250o

F4 = 40 N 4 = 300o

θsinF θcosF kkkk

43.3 25.070.7 70.710.3 28.220.0 34.6

17.7 32.9

22R 9.327.17F

N 4.37FR

Vectors

22R 9.327.17F

N 4.37FR

9.32tan

9.32tan 1 o7.61

FR = 37.4 N

180R 7.61180

oR 118

Vectors

F1 = 90 N 1 = 45o

F2 = 80 N 2 = 150o

F3 =50 N 3 = 220o

F4 = 70 N 4 = 340o

θsinF θcosF kkkk

63.669.338.365.8

63.640.0

23.923.9

21.8 47.6

22R 6.478.21F

N 4.52FR

8.216.47

tan 1R

oR 4.65

FR = 52.4 N

Introduction to Vectors. Vectors ScalarsVectors Distance Time Mass Work Energy Speed Displacement...

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Transcript of Introduction to Vectors. Vectors ScalarsVectors Distance Time Mass Work Energy Speed Displacement...

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