AP Physics C
Vector review and 2d motion
The
The
good
Bad news
news
•• 2d
You
motion
will follow
problems
all oftake
the same
twicerules
as many
yousteps.
used
in 1d motion.
It allows
to more
realistic and
•• 2d
motionour
Canproblems
become more
confusing
interesting
• Requires a good understanding of Vectors
My hair is
Remember: Vectors are… very
Vectory!!
Any value with a direction
and a magnitude is a
considered a vector.
Velocity,
displacement,
and
acceleration,
are all
vectors.
#3
The “opposite” of a
Vector is a Scalar.
A Scalar is a value
with a magnitude
but not a direction!
Example #2: Speed!
#4
If you are dealing
with 2 or more
vectors we need to
find the “net”
magnitude….
#5
#6
What about these?
How do we find our
“net” vector?
These vectors have a
magnitude in more
than one
dimension!!!
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 xaxis of the yellow vector.
The white vector,
positioned as a shadow on
the y-axis, is the ycomponent of the yellow
vector.
Think about this as if you are
going to your next class. You
can’t take a direct route even
if your Displacement Vector
winds up being one!
• Two Ways:
1. Graphically: Draw vectors to scale, Tip to
Tail, and the resultant is the straight line
from start to finish
2.Mathematically: Employ vector math
analysis to solve for the resultant vector
and write vector using “unit components”
Example…
1st: Graphically
• A = 5.0 m @ 0°
• B = 5.0 m @ 90°
• Solve A + B
R
Start
R=7.1 m @ 45°
Important
• You can add vectors in any order and yield the
same resultant.
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
Vectors
be added
mathematically
adding
only can
purpose
is to show
dimension. by
They
are
Unit(^)
components.
shown withtheir
“hats”
rather than arrows. I
will show them in bold.
Add vectors A and B to find the resultant vector C given
the following…
A = -7i + 4j and B = 5i + 9j
A.
B.
C.
D.
C = -12i + 13j
C = 2i + 5j
C = -2i + 13j
C = -2i + 5j
Multiplying Vectors (products)
3 ways
1. Scalar x Vector = Vector w/
magnitude multiplied by the value of
scalar
A = 5 m @ 30°
3A = 15m @ 30°
Example: vt=d
Multiplying Vectors (products)
2. (vector) • (vector) = Scalar
This is called the Scalar Product or the
Dot Product
Dot Product Continued (see p. 25)
B
Φ
A
Multiplying Vectors (products)
3. (vector) x (vector) = vector
This is called the vector product or the
cross product
Cross Product Continued
Cross Product Direction and
reverse