Relative Motion by fhSiUpI

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• pg 1
```									AP Physics C
Mrs. Coyle
• Coordinate Systems
• Vectors and Scalars
• Properties of Vectors
• Unit Vectors
Coordinate Systems

• Cartesian (rectangular) Coordinates
(x,y)

• Polar Coordinates          (r, θ)
– θ is taken to be positive
counterclockwise from the +x axis.
Vectors and Scalars
• Scalars- magnitude only

• Vectors- magnitude and direction
Equality of Vectors
• Two vectors are equal if they have
the same magnitude and direction.
• Graphical
• Algebraic

• Resultant: sum of vectors
Properties of Vector

•A + B = B + A

•(A + B) + C = A + (B + C)
Vectors

• Parallelogram Method
Vectors
• Vectors are moved parallel to themselves so
that they are positioned in such a way that
other.
• The resultant is drawn by starting at the
first tail (loose tail) and ending (arrow head
B
A

Resultant

• Parallelogram Method
• The vectors are placed tail to tail forming a
rectangle.
• The diagonal that starts at the joint tails
has its tail at the joint tails) is the
resultant.
A
Resultant

B
Graphical Vector
Subtraction
When subtracting A-B :

• Invert vector B to get -B
Component Method
1)Find x and y components of each
vector.
ax = acosθ

ay = a sinθ
Component Method Cont’d

3)Use the Pythagorean Theorem to find
the magnitude of the resultant.

4)Use q=tan-1 |Y | to find the direction
X
with respect to the x-axis.
Unit Vectors:         î, ĵ, k
• Dimensionless vector with a
magnitude of 1.

• They specify direction x, y, z

• Example: A= 2 î + 3 ĵ - 6k
Example 1
A= 10 î - 1 ĵ - 6k
B= - 6î + 5 ĵ + 6k
Give the components of the
resultant vector, its magnitude and
its direction with respect to the x-
axis.

Answer: R= 4î + 4ĵ, 5.7, 45 deg above +x
axis
Example 2
The position vector as a function of
time for an object is given by
r(t)= 2 î + 3t ĵ - 6k,
r is in meters and t is in seconds.

Evaluate dr/dt and explain what is its
significance?
Example 3
• These are instructions for finding a
treasure : Go 75.0 paces at 240°,
turn to 135° and walk 125 paces,
then travel 100 paces at 160°. The
angles are measured ccw from the
east, the +x direction. Determine the
resultant displacement from the
starting point.

• Answer: 227 paces at 165°