VECTORS

Vectors Vectors have magnitude and direction They are represented by an arrow-tipped line segment( ) The length (drawn to scale) represents the magnitude of the quantity The direction of the arrow represents the direction of the quantity

Vectors Vector Addition in One Dimension Add by placing the tail of one vector to the head of another: The resultant represents the sum of the two Resultant – vector sum of the component vectors **order of addition of vectors does not matter**

Vectors Vector Addition in Two Dimensions Place the tail of one vector to the head of another. Draw the resultant from the tail of the FIRST vector to the head of the LAST

Vectors Graphical Addition of Vectors Follow the same rules for vector addition, however, everything is drawn to scale… Set up an appropriate scale (1cm=1m) Draw the vectors to scale with a ruler, and use a protractor to measure the correct angle Once the resultant is drawn, measure it with a ruler and convert using your scale. Measure the angle of the resultant counterclockwise from 0° (east)

Vectors Analytical Addition of Vectors (2 vectors) Set up the vectors head to tail Use the Law of Cosines to find the resultant c2 = a2 + b2 –2ab cosine C OR Use the Law of Sines to find the resultant sine A/a = sine B/b = sine C/c

Vectors Analytical Addition of Vectors continued… If the vectors form a RIGHT triangle(90°) when placed head to tail, use the SOCATOA method and Pythagorean Theorem: sin  = opp/hyp cos = adj/hyp tan  = opp/adj a2 + b2 = c2

Vectors Components of Vectors You can resolve a vector triangle using the resultant and working backwards Choose two components (sides) that are perpendicular to one another(90°) One component is the x-component and one component is the y-component

Vectors Components cont. x= R cos y = R sin  Calculate all of the x and y components Sum all of the x components; sum all of the y components Since x and y form a right triangle, use Pythagorean theorem to calculate the resultant…(see sheet for component method)