Post on 24-Dec-2015
AP Physics CAP Physics C
Vector review and 2d motionVector review and 2d motion
The good newsThe good news
• You will follow all of the same rules you used in 1d motion.
• It allows our problems to more realistic and interesting
The Bad newsThe Bad news
• 2d motion problems take twice as many steps.
• 2d motion Can become more confusing
• Requires a good understanding of Vectors
Remember: Vectors are…
Any value with a direction and a magnitude is a
considered a vector.
My hair is very
Vectory!!
Velocity, displaceme
nt, 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 If you are dealing with 2 or more with 2 or more vectors we need to vectors we need to find the “net” find the “net” magnitude….magnitude….
#5
What about these? What about these? How do we find our How do we find our “net” vector?“net” vector?
These vectors have a magnitude in more than one dimension!!!
#6
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
can’t take a direct route even if your Displacement Vector
winds up being one!
Analytic analysis: Unit components
• 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.
• a vector can be written as the sum of its components
Analytic analysis: Unit components
A = Axi + AyjThe 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.
Add vectors A and B to find the resultant vector C given the following…
A = -7i + 4j and B = 5i + 9j
A. C = -12i + 13j
B. C = 2i + 5j
C. C = -2i + 13j
D. 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)
Φ
A
B
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