Vectors
Scalar Terms ( Magnitude only) Magnitude=quantitave measure or in simple terms, a number. Time Distance Speed Mass
Vector Terms (Magnitude and Direction) Displacement Velocity Acceleration
Adding Vectors Vectors are represented by arrows The size of the vector tells you about the amount of the quantity Always add head to tail Resultant- the vector that represents the sum of two or more vectors
Adding Vectors 6m 1m Now add from head to tail We add 6m +1m=7m 5m 2m Now we add from head to tail The resultant vector is 5m-2m=3m
At an angle
To find components Hypotenuse Opposite Adjacent To find components, you must use trigonometric functions Hypotenuse Opposite ø Adjacent
Trig functions Θ is the angle between the vector and the x axis sin Θ = _opposite_ hypotenuse cos Θ = _adjacent_ tan Θ = _opposite_ adjacent
Steps for finding the components Draw a picture (arrowheads, original vector & components) Choose a trig function Use algebra to solve for the desired variable & plug in Calculator in degrees! Check with Pythagorean theorem
Example
X component cos Θ = _adjacent_ hypotenuse cos 35 = _adjacent_ 316 259 N = adjacent
Y component sin Θ = _opposite_ hypotenuse sin 35 = _opposite_ 316
How to find components when you add two vectors Find the x and y component for both vectors Add up the x components Add up the y components Draw a new set of vectors Use Pythagorean theorem to get the magnitude of the resultant vector Use arctangent to get the angle of the new vector
To find the angle of the resultant vector Use arctangent function: Θ = tan-1 (opp/adj) Θ = tan-1 (30.2/9.1) Θ = tan-1 (3.3) Θ = 73.1°
Formulas a2 + b2 = c2 R2 = a2 + b2 - 2ab(cosθ) SOH CAH TOA