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AP Physics C

AP Physics C. Vector review and 2d motion. The Bad news. The good news. 2d motion problems take twice as many steps. 2d motion Can become more confusing Requires a good understanding of Vectors. You will follow all of the same rules you used in 1d motion.

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AP Physics C

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  1. AP Physics C Vector review and 2d motion

  2. The Bad news The good news • 2d motion problems take twice as many steps. • 2d motion Can become more confusing • Requires a good understanding of Vectors • You will follow all of the same rules you used in 1d motion. • It allows our problems to more realistic and interesting

  3. My hair is very Vectory!! Remember: Vectors are… Any value with a direction and a magnitude is a considered a vector. #3 Velocity, displacement, and acceleration, are all vectors.

  4. For Example!! The “opposite” of a Vector is a Scalar. A Scalar is a value with a magnitude but not a direction! #4 Example #2: Speed!

  5. Simple Addition of Vectors!! If you are dealing with 2 or more vectors we need to find the “net” magnitude…. #5

  6. Not so Simple #6 Addition of Vectors!! What about these? How do we find our “net” vector? These vectors have a magnitude in more than one dimension!!!

  7. 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 can’t take a direct route even if your Displacement Vector winds up being one!

  8. 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…

  9. 1st: Graphically • A = 5.0 m @ 0° • B = 5.0 m @ 90° • Solve A + B R R=7.1 m @ 45° Start

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

  11. 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.

  12. Add vectors A and B to find the resultant vector C given the following…A = -7i + 4j and B = 5i + 9j • C = -12i + 13j • C = 2i + 5j • C = -2i + 13j • C = -2i + 5j

  13. Multiplying Vectors (products)3 ways • Scalar x Vector = Vector w/ magnitude multiplied by the value of scalar A = 5 m @ 30°3A = 15m @ 30° Example: vt=d

  14. Multiplying Vectors (products) 2. (vector) • (vector) = Scalar This is called the Scalar Product or the Dot Product

  15. Dot Product Continued (see p. 25) B Φ A

  16. Multiplying Vectors (products) • (vector) x (vector) = vector This is called the vector product or the cross product

  17. Cross Product Continued

  18. Cross Product Direction and reverse

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