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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!
1204@Rd ��������������
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
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