Physics 101: Lecture 4, Pg 1 Lecture 4: PHY101 Chapter 1 : Scalars and Vectors (1.5) Chapter 2: Distance and Displacement, Speed and Velocity (2.1,2.2)

Physics 101: Lecture 4, Pg 2 Vectors Vectors are graphically represented by arrows:  The direction of the physical quantity is given by the direction of the arrow.  The magnitude of the quantity is given by the length of the arrow.

Physics 101: Lecture 4, Pg 3 Addition of Vectors l Graphical: Tail-to-head method l Resultant of Forces (Addition of Vectors) Resultant of Forces (Addition of Vectors)

Physics 101: Lecture 4, Pg 4 Graphical Method - Example You are told to walk due east for 50 paces, then 30 degrees north of east for 38 paces, and then due south for 30 paces. What is the magnitude and direction of your total displacement ?

Physics 101: Lecture 4, Pg 5 Addition of Vectors l Using components (A,B lie in x,y plane): C = A+B = A x + A y + B x + B y = C x +C y Cx and Cy are called vector components of C. They are two perpendicular vectors that are parallel to the x and y axis. A x,A y and B x, B y are vector components of A and B.

Physics 101: Lecture 4, Pg 6 Scalar Components of a Vector (in 2 dim.) l Vector components of vector A: A = A x +A y l Scalar components of vector A: A = A x x +A y y A x and A y are called scalar components of A. x and y are unit vectors. Equivalently: A=(A x,A y ) A is a vector pointing from the origin to the point with coordinates A x,A y.

Physics 101: Lecture 4, Pg 7 Scalar Components of a Vector (in 2 dim.) l Scalar components of vector A: A = A x x +A y y | A|,  known: |A x |= |A| Cos  |A y |=|A| Sin  A x, A y known: A 2 =(A x ) 2 +(A Y ) 2  = Tan -1 |A y |/|A x |

Physics 101: Lecture 4, Pg 8 Addition of Vectors l Using scalar components (A,B lie in x,y plane): C = A+B = A x x + A y y+ B x x+ B y y= C x x+C y y 1. Determine scalar components of A and B. 2. Calculate scalar components of C : C x = A x +B x and C y =A y +B y 3. Calculate |C| and  : C 2 =(C x ) 2 +(C Y ) 2  = Tan -1 |C y |/|C x |

Physics 101: Lecture 4, Pg 9 Addition of Vectors l vector sum vector sum

Physics 101: Lecture 4, Pg 10 Displacement and Distance l Displacement is the vector that points from a body’s initial position to its final position. The length of is equal to the shortest distance between the two positions.  x = x –x 0 The length of  x is not the same as distance traveled !

Physics 101: Lecture 4, Pg 11 Average Speed and Velocity l Average velocity describes how the displacement of an object changes over time: average velocity = displacement/elapsed time v = (x-x 0 ) / (t-t 0 ) =  x /  t Average velocity also takes into account the direction of motion. The magnitude of v is not the same as the average speed !

Physics 101: Lecture 4, Pg 12 Summary of Concepts l kinematics: A description of motion l position: your coordinates l displacement:  x = change of position l velocity: rate of change of position average :  x/  t instantaneous: slope of x vs. t l acceleration: rate of change of velocity average:  v/  t instantaneous: slope of v vs. t

Physics 101: Lecture 4, Pg 13 Lecture 3: Scalars and Vectors Distance and Displacement, Speed and Velocity I strongly suggest that you try the example problems in the textbook. If you have trouble with any of them, please go to office hours for help!