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