Vector Scalar Quantities Characteristics of a Scalar Quantity

Vector & Scalar Quantities

Characteristics of a Scalar Quantity o o Only has magnitude Requires 2 things: 1. A value 2. Appropriate units Ex. Mass: 5 kg Temp: 21° C Speed: 65 mph

Characteristics of a Vector Quantity o o Has magnitude & direction Requires 3 things: 1. A value 2. Appropriate units 3. A direction! Ex. Acceleration: 9. 8 m/s 2 down Velocity: 25 mph West

More about Vectors o A vector is represented on paper by an arrow 1. the length represents magnitude 2. the arrow faces the direction of motion 3. a vector can be “picked up” and moved on the paper as long as the length and direction its pointing does not change

Understanding Vector Directions To accurately draw a given vector, start at the second direction and move the given degrees to the first direction. N W 30° N of E E Start on the East origin and turn 30° to the North S

Graphical Addition of Vectors 5 Km Scale: 1 Km = 1 cm 3 Km Resultant Vector (red) = 6 cm, therefore its 6 km.

Vector Addition Example #1 o Use a graphical representation to solve the following: A hiker walks 1 km west, then 2 km south, then 3 km west. What is the sum of his distance traveled using a graphical representation?

Vector Addition Example #1 (cont. ) Answer = ? ? ? ?

Mathematical Addition of Vectors o Vectors in the same direction: Add the 2 magnitudes, keep the direction the same. Ex. + = 3 m E 1 m E 4 m E

Mathematical Addition of Vectors o Vectors in opposite directions Subtract the 2 magnitudes, direction is the same as the greater vector. Ex. 4 m S + 2 m N = 2 m S

Mathematical Addition of Vectors o Vectors that meet at 90° Resultant vector will be hypotenuse of a right triangle. Use trig functions and Pythagorean Theorem.