Ch 3 Vectors

Vector vs. Scalar

• State whether each of the following quantities is a vector or a scalar:

Position AccelerationVelocity

SpeedDisplacement

Distance

Force

Energy

Temperature

Volume

Vector Vector Scalar

Scalar Scalar

Scalar Scalar

Vector

Vector Vector

Pressure

Vector

Adding Vectors Graphically• You walk 5m @ 0o and then turns to walk 6m @90o.

Finally, you turn to walk 8 m at 200°. What is your displacement?

Addition is commutative!

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Independence of Vectors

• Perpendicular vector quantities are independent of each other.

• For example in projectile motion– Vx Velocity in the X-direction

– Vy Velocity in the Y-direction

Are independent of each other.

Components of Vectors

Finding the vector magnitude and direction when you know the components.

Recall: is measured from the positive x axis.

22yx AAA

1tan tany y

x x

A A

A A

Caution: Beware of the tangent function.

Always consider in which quadrant the vector lies when dealing with the tangent function.

III

III IV

8.66

5

1tan (5 / 8.66) 30

-8.66

5

1tan (5 / 8.66)

30

-8.66

-5

1tan ( 5 / 8.66)

30

150

210

8.66

-5

1tan ( 5 / 8.66) 30

330

Adding Vectors Analytically

• Resolve each vector into its horizontal and vertical components

• Add all of the vertical components together

• Add all of the horizontal components together

• Draw a right triangle using the horizontal and vertical resultants

Adding Vectors Analytically

Magnitude Angle X component Y component

4.5N 30o 3.89N 2.25N

7N 210o -6.06N -3.5N

6N 150o -5.19N 3.0N

--------------- ------------ Rx=-7.36N Ry=1.7N

cosxA A 4.5 @30oA N

7 @ 210oB N

6 @150oC N

sinyA A cosxB B cosxC C

sinyB B sinyC C

R=7.55N Angle =-13o+180o = 167o