AP Physics C Vector review and 2d motion

The 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 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, 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

What about these? How do we find our “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…

1 st : Graphically A = 5.0 0° B = ° Solve A + B R Start R=7.1 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 = A x i + A y j 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.

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 30° 3A = 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