1. Two-Dimensional Motion and Vectors
Introduction to Vectors

2. Scalars and Vectors
Every physical quantity can be described as a vector or a scalar
Scalar – a physical quantity that has only magnitude, but no direction
Speed, distance
Vector – a physical quantity that has both magnitude and direction
Velocity, displacement

3. Scalars and Vectors
The book uses bold to represent vectors and italics to represent scalars
Can also use directional arrows to denote vectors v

4. Vector Diagrams Use arrows to show direction
Length of arrow shows relative strength of vector
Long arrow has greater magnitude than short arrow

5. Vector Addition
Can only add vectors with the same units and that describe similar quantities
Cannot add displacement and velocity vectors
Resultant – a vector representing the sum of two or more vectors

6. Triangle Method of Addition of Vectors
Add vectors by drawing a to-scale diagram
Measure the straight line distance from the tail of the initial vector to the head of the final vector
Multiply by the scale
Use a protractor to determine the direction of the resultant

7. Vector Addition
Vectors can be moved parallel to themselves in a diagram
Must remain pointing in the same direction
Vectors can be added in any order
Total displacement remains the same
To subtract vectors – add the opposite
A vector plus its opposite results in zero

8. Vector Addition

9. Vector Multiplication and Division
Multiplying and dividing vectors by scalars results in vectors
A cab driver is told to drive twice as fast
Original velocity vcab is multiplied by scalar number 2
Result is 2vcab
Twice as fast in opposite direction would be -2vcab