Unit III Part A- Vectors

Basic Vector Info We know of two ways to measure quantities, scalar and vector Scalar quantities are described by their magnitude (amount) only. This means they have a number and a unit. Vector quantities have more. They have an amount and a direction. You must be able to tell if quantities are vector or scalar.

Here are some lists: These quantities are scalar: Mass, distance, time, volume, speed, energy and work These quantities are vector: Velocity, momentum, acceleration, displacement, magnetic field strength

These lists are not complete These lists are not complete. You can figure out if a measurement is vector or scalar easily, just look at the components of the measurement (i.e. the equation). If it has vectors in it, then it’s a vector quantity. If it doesn’t then its scalar.

Some quantities are measured in both scalar and vector terms Some quantities are measured in both scalar and vector terms. These include: Scalar Vector Distance displacement Speed Velocity Ex. 1.)A distance of 10m is scalar A displacement of 10m East is vector 2.) A speed of 26m/s is scalar A velocity of 26m/s NW is vector.

Shortcuts Scalar quantities are amounts. Vector quantities are amounts with direction. Scalar quantities are added, subtracted, multiplied and divided using normal methods. Vector quantities must be added, subtracted using different methods.

Adding and Resolving (subtracting) vectors Vectors should be drawn as rays, with an arrowhead pointing in the direction of the quantity described. Ex. 20m/s North as a vector 20m/s Vectors may be added using various methods. One such method is call “The tip-to-tail method”

Rules for adding vectors using “The tip-to-tail Method” 1.) Draw both vectors to the same scale 2.) Choose either vector to draw first, then draw your 2nd vector from the tip (arrowhead) of the first. 3.) Use a protractor to find the correct angles 4.) The sum (called the resultant) of the two vectors will be the 3rd side of the triangle. Component + component = resultant

Ex: Add the following pairs of vectors: 25m/s N + 28m/s 450 NE 36m/s2 N + 21 m/s2, 560 SW Sometimes if the vectors make right angles with each other, you can add them up using Pythagorean Theorem. (Also remember your perfect triangles!) Ex. Add the following pairs of vectors: 10m/s E + 8 m/s N 5m/s W + 12 m/s S

Other types of problems will show you vectors, then you have to add them and describe the resultant. Remember to add the vectors “tip to tail” Ex. What is the resultant of the following pairs of vectors? A. B. C.

Resolving Vectors Sometimes known as Vector subtracting, it basically involves finding one of the components of a resultant vector. Can be compared to finding the unknown in an equation like this: 4x__=24. You are finding one of the numbers that will make 24. You may be asked to find one or both components of the given vector. This is easily done using your trig functions.

Look at the diagram below: Formulas: Ay = Asin0 (vertical) Ax = Acos0 (horizontal) Look at the diagram below: 25m/s A velocity vector has been drawn at an angle of 60 degrees. What are its horizontal and vertical components? 60

Try These Other Examples Find the horizontal component of an acceleration vector of 120 m/s2 at an angle of 670 What is the vertical component of a velocity vector of 21 m/s drawn 320 from the horizon? **As in adding vectors, resolving problems may be found in diagram form.

Which pair of vectors would have a resultant of A. B. C. D. What is the vector that will be the 2nd component for this pair? Resultant component