1. Role of units in problem solving Trigonometry Scalars and Vectors Vector Addition and Subtraction Addition of Vectors by Components

2.  SI units for mass, length, and time are the kilogram, meter, and second.  Only SI units, base and derived, are used on the AP Physics B exam.  *You will often need to be able to determine the validity of equations by analyzing the dimensions of the quantities involved.  Example: Pg. 21, #7

3.  Trigonometry is the study of triangles, often right triangles.  Lengths of the sides of a right triangle can be used to define some useful relationships called sine, cosine, and tangent.  The trig relationships will be particularly helpful when dealing with vectors.  Example: pg. 21, #11

4.  A scalar is a quantity which has no direction associated with it, only magnitude: mass, volume, time, temp, distance, speed, work, energy.  A vector is a quantity which has both magnitude (size) and direction (angle): displacement, velocity, acceleration, force, weight, momentum.  We can graphically add vectors to each other by placing the tail of one vector onto the tip of the previous vector.  Example: #4- white board  Example: pg 22, #23

5.  Resultant vector- displacement from the origin to the tip of the last vector, it is equal to the vector sum of the individual vectors  Adding displacement vectors in any order will achieve the same resultant. Thus, the addition of vectors is commutative.  Equilibrant vector- can cancel or balance the resultant vector, it is equal in magnitude and opposite in direction of the resultant vector.  Example: pg 22, #25

6.  We may work with vectors mathematically by breaking them into their components. Vector A can have the x-axis component A x and its y- axis component A y. (white board sketch)  We can use trigonometry to find the magnitudes of these different components.  Example: pg 23, # 33

7.  Earlier we added vectors together graphically. We can also use the components to find the resultant of any number of vectors.  Example: Add A+B+C  A= 4 meters at 30 degrees from the x-axis (NE)  B = 3 meters at 45 degrees from the x-axis (NE)  C = 5 meters at 25 degrees from the y- axis (in the south/west direction)  The properties of vectors can be applied to any vector.  Example: pg 23, #41  Time permitting: pg 23, #65