Chapter 3 Notes

Coordinate Systems—Cartesian (for 2 dimensions and 3 dimensions)
o
Origin
 fixed point of reference
o
Axes
 scales and labels
o
Instructions
 how to label a point relative to origin and axes
o
It’s basically a grid
x
is positive to the left,
y
is positive up
Find ourselves by finding a pair of 2 numbers (
x
,
y
)
o
For
3
dimensions you add the z coordinate (thus having 3 numbers)

Polar Coordinate System
o
=
x
r cosθ
o
=
y
r sinθ
o
=
tanθ
yx
o
=
+
r
x2
y2

Vectors and Scalars (used for multiple dimensions)
o
A
scalar quantity
is completely specified by a single value with the
appropriate units and has not direction
o
Vector Quantity
It is completely described by a number and appropriate units plus a
direction
o
Vector example
A particle travels from A to B along the path shown by the dotted line
•
This is the
distance
traveled and is a
scalar
The
displacement
is the solid line from A to B
•
The displacement is independent of the path taken between the two
points
•
Displacement is a
vector
o
Vector Representation
Bold letter =
A
Letters with arrow =
A
Magnitude =
A
•
Magnitude shown as the nonbold letter for vector
o
A
instead of
A
o
Vector Addition
Draw vectors “tail to tip”
The resultant (
R
) is drawn from the tail of
A
to the tip of the last vector (
B
)
R
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•
θ
B
Law of Cosines useful for getting magnitude when angles known
•
=
+

R2
A2
B2
2ABcosθ
The two sums are the same vector
•
=
+
+
A
B
C
+
D
•
=
B
+
+
+
C
D A
Example
•
12. A car travels 20.0 km due north and then 35.0 km in a direction
60.0º west of north.
Find the magnitude and direction of the car’s
resultant displacement
Vector Addition/Subtraction Rules
•
The sum of 2 vectors is independent of the order of the addition
o
Commutative Law of Addition
+
=
+
A
B
B
A
•
The sum of 3 or more vectors is independent of how they are grouped
o
Associative Law of Addition
+
+
=
+
+
A
B
C
A
B
C
•
All of the vectors must have the same units
•
All of the vectors must be of the same type of quantity
you cannot
add a displacement to a velocity!
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 Winter '08
 DISHAW
 Physics, Acceleration, Force, Velocity, Unit Vectors Unit, vector o Vector

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