AP Physics C

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AP Physics C

• Vector review and 2d motion

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The good news
The Bad news

• You will follow all of the same rules you used in
  1d motion.
• It allows our problems to more realistic and
  interesting

• 2d motion problems take twice as many steps.
• 2d motion Can become more confusing
• Requires a good understanding of Vectors

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My hair is very Vectory!!
Remember Vectors are Any value with a
direction and a magnitude is a considered a
vector.
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Velocity, displacement, and acceleration, are all
vectors.
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For Example!!
The opposite of a Vector is a Scalar. A
Scalar is a value with a magnitude but not a
direction!
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Example 2 Speed!
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Simple
Addition of Vectors!!
If you are dealing with 2 or more vectors we need
to find the net magnitude.
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Not so Simple
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Addition of Vectors!!
What about these? How do we find our net
vector?
These vectors have a magnitude in more than one
dimension!!!
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Analytic analysis Unit components
In this picture, a two dimensional vector is
drawn in yellow. This vector really has two
parts, or components. Its x-component, drawn in
red, is positioned as if it were a shadow on the
x-axis of the yellow vector. The white vector,
positioned as a shadow on the y-axis, is the
y-component of the yellow vector.
Think about this as if you are going to your next
class. You cant take a direct route even if
your Displacement Vector winds up being one!
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Addition of Vectors!!

• Two Ways
• Graphically Draw vectors to scale, Tip to Tail,
  and the resultant is the straight line from start
  to finish
• Mathematically Employ vector math analysis to
  solve for the resultant vector and write vector
  using unit components
• Example

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(No Transcript)
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1st Graphically

• A 5.0 m _at_ 0
• B 5.0 m _at_ 90
• Solve A B

R
R7.1 m _at_ 45
Start
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Important

• You can add vectors in any order and yield the
  same resultant.

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Analytic analysis Unit components

• a vector can be written as the sum of its
  components

A Axi Ayj
The letters i and j represent unit Vectors They
have a magnitude of 1 and no units. There only
purpose is to show dimension. They are shown
with hats () rather than arrows. I will show
them in bold.
Vectors can be added mathematically by adding
their Unit components.
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Add vectors A and B to find the resultant vector
C given the followingA -7i 4j and B
5i 9j

1. C -12i 13j
2. C 2i 5j
3. C -2i 13j
4. C -2i 5j

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Multiplying Vectors (products)3 ways

• Scalar x Vector Vector w/ magnitude multiplied
  by the value of scalar A 5 m _at_ 303A 15m
  _at_ 30
• Example vtd

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Multiplying Vectors (products)

• 2. (vector) (vector) Scalar
• This is called the Scalar Product or the Dot
  Product

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Dot Product Continued (see p. 25)
B
F
A
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Multiplying Vectors (products)

• (vector) x (vector) vector
• This is called the vector product or the cross
  product

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Cross Product Continued
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Cross Product Direction and reverse