Lecture 4: PHY101VectorsAddition of VectorsGraphical Method - ExampleSlide 5Scalar Components of a Vector (in 2 dim.)Slide 7Slide 8Slide 9Displacement and DistanceAverage Speed and VelocitySummary of ConceptsLecture 3:Physics 101: Lecture 4, Pg 1Lecture 4: PHY101Chapter 1 :•Scalars and Vectors (1.5)Chapter 2:•Distance and Displacement, Speed and Velocity (2.1,2.2)Physics 101: Lecture 4, Pg 2VectorsVectorsVectors 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 3Addition of VectorsAddition of VectorsGraphical: Tail-to-head methodResultant of Forces (Addition of Vectors)Physics 101: Lecture 4, Pg 4Graphical Method - ExampleGraphical Method - ExampleYou are told to walk due east for 50 paces, then 30 degrees north of east for 38 paces, and then due southfor 30 paces.What is the magnitude and direction of your totaldisplacement ?Physics 101: Lecture 4, Pg 5Addition of VectorsAddition of VectorsUsing components (A,B lie in x,y plane): C = A+B = Ax + Ay + Bx + By = Cx+Cy Cx and Cy are called vector components of C.They are two perpendicular vectors that are parallel to the x and y axis. Ax,Ay and Bx, By are vector components of A and B.Physics 101: Lecture 4, Pg 6Scalar Components of a Vector (in 2 Scalar Components of a Vector (in 2 dim.)dim.)Vector components of vector A: A = Ax +AyScalar components of vector A: A = Ax x +Ay yAx and Ay are called scalar components of A. x and y are unit vectors.Equivalently:A=(Ax,Ay) A is a vector pointing from theorigin to the point with coordinates Ax,Ay.Physics 101: Lecture 4, Pg 7Scalar Components of a Vector (in 2 Scalar Components of a Vector (in 2 dim.)dim.)Scalar components of vector A: A = Ax x +Ay y |A|, known: |Ax|= |A| Cos |Ay|=|A| Sin Ax, Ay known: A2=(Ax )2+(AY)2 = Tan-1 |Ay|/|Ax|Physics 101: Lecture 4, Pg 8Addition of VectorsAddition of VectorsUsing scalar components (A,B lie in x,y plane): C = A+B = Ax x + Ay y+ Bx x+ By y= Cx x+Cy y 1. Determine scalar components of A and B. 2. Calculate scalar components of C : Cx = Ax+Bx and Cy=Ay+By3. Calculate |C| and :C2=(Cx )2+(CY)2 = Tan-1 |Cy|/|Cx|Physics 101: Lecture 4, Pg 9Addition of VectorsAddition of Vectorsvector sumPhysics 101: Lecture 4, Pg 10Displacement and DistanceDisplacement and DistanceDisplacement 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 –x0The length of x is not the same as distance traveled !Physics 101: Lecture 4, Pg 11Average Speed and VelocityAverage Speed and VelocityAverage velocity describes how the displacement of an object changes over time: average velocity = displacement/elapsed time v = (x-x0) / (t-t0) = 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 12Summary of Concepts Summary of Concepts kinematics: A description of motionposition: your coordinatesdisplacement: x = change of positionvelocity: rate of change of position•average : x/t•instantaneous: slope of x vs. tacceleration: rate of change of velocity•average: v/t•instantaneous: slope of v vs. tPhysics 101: Lecture 4, Pg 13Lecture 3: Lecture 3: •Scalars and Vectors•Distance and Displacement, Speed and VelocityI strongly suggest that you try the example problems in the textbook.If you have trouble with any of them, pleasego to office hours for
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