1. Two-Dimensional Motion and Vectors Chapter 02 Honors PhysicsLongmeadow High School Chapter 02 – Two-Dimensional Motion and Vectors

2. 2-1Scalars and Vectors Defined Chapter 02 – Two-Dimensional Motion and Vectors A scalar quantity is a physical quantity that can be completely described by its magnitude A vector quantity is a physical quantity with both a magnitude and a directed associated with it

3. 2-2Examples of Scalar and Vector Quantities Chapter 02 – Two-Dimensional Motion and Vectors ScalarsVectors Temperature (˚F or ˚C)Displacement (m) Number of Gas Molecules in a ContainerVelocity (m/s) Volume (m 3 )Acceleration (m/s 2 ) Mass (kg)Force (N) Distance (m)Momentum (kg·m/s) Speed (m/s)Torque (N·m) Work (J)Electric Field (N/C) Power (W) Kinetic Energy (J) Potential Energy (J) Electric Charge (C) Electric Current (A)

4. 2-3Representing Vectors Chapter 02 – Two-Dimensional Motion and Vectors Textbook and Typed Media – Boldface indicates a vector quantity v = 3.5 m/s at 30˚ – Italics indicate a scalar quantity v = 3.5 m/s where v = |v| Handwritten / Blackboard – Arrow above abbreviation indicates vector quantity v = 3.5 m/s at North

5. 2-4Describing Vectors Graphically Chapter 02 – Two-Dimensional Motion and Vectors Vectors are depicted as arrows with the tip of the arrow indicating the direction of the vector A vector has both a tail and a tip The length of the arrow is proportional to its magnitude The direction of a vector is typically given with respect to the horizontal axis “…walks 5 km 30˚ north of east” Be on the look out for alternative descriptions “east of north”

6. 17-2Resolving Vectors into Components Chapter 02 – Two-Dimensional Motion and Vectors 6

7. 2-5Resolving Vectors into Components Chapter 02 – Two-Dimensional Motion and Vectors 7

8. 2-6Combining Scalars and Vectors Chapter 02 – Two-Dimensional Motion and Vectors Vector quantities are distinct from scalar quantities – they combine differently. We’re used to combining scalars: – The sum of two scalars results in a: scalar – The product of two scalars results in a: scalar Now consider vectors – they can combine with scalars as well as with other vectors – The sum of two vectors results in a: vector – The product of a scalar and a vector results in a: vector Think about what “scaling” a vector might look like – The product of two vectors results in: well, that depends There are not one, but two different ways in which to multiply vectors – one resulting in a scalar (scalar product) and another resulting in a vector (vector product)

9. 2-7Scalar Multiplication Chapter 02 – Two-Dimensional Motion and Vectors Negative of a Vector

10. 2-8Vector Addition: Parallelogram Method Chapter 02 – Two-Dimensional Motion and Vectors Draw vectors A and B such that they share a common tail. Taking these two vectors to be two adjacent sides of a parallelogram, draw the resultant vector as the diagonal

11. 2-9Vector Addition: Tail-to-Tip/Head-To-Tail Method Chapter 02 – Two-Dimensional Motion and Vectors Start by placing any vector with its tail at the origin Place the tail of the next vector to the tip of the previous vector After doing this for all vectors, the resultant vector is found by drawing a straight line from the tail of the first vector to the tip of the last vector.