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Lecture 4: PHY101

Lecture 4: PHY101. Chapter 1 : Scalars and Vectors (1.5) Chapter 2: Distance and Displacement, Speed and Velocity (2.1,2.2). Vectors. Vectors are graphically represented by arrows: . The direction of the physical quantity is given by the direction of the arrow.

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Lecture 4: PHY101

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

  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.

  3. Addition of Vectors • Graphical: Tail-to-head method • Resultant of Forces (Addition of Vectors)

  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 ?

  5. Using 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. Addition of Vectors

  6. Scalar Components of a Vector (in 2 dim.) • Vector components of vector A: A = Ax +Ay • Scalar components of vector A: A = Axx +Ayy Ax and Ay are called scalar components of A. x and y are unit vectors. Equivalently: A=(Ax,Ay) A is a vector pointing from the origin to the point with coordinates Ax,Ay.

  7. Scalar Components of a Vector (in 2 dim.) • Scalar components of vector A: A = Axx +Ayy |A|, q known: |Ax|= |A| Cos q |Ay|=|A| Sin q Ax, Ay known: A2=(Ax )2+(AY)2 q= Tan-1 |Ay|/|Ax|

  8. Using scalar components (A,B lie in x,y plane): C = A+B = Axx + Ayy+ Bxx+ Byy= Cxx+Cyy 1. Determine scalar components of A and B. 2. Calculate scalar components of C : Cx = Ax+Bx and Cy=Ay+By 3. Calculate |C| and q : C2=(Cx )2+(CY)2q= Tan-1 |Cy|/|Cx| Addition of Vectors

  9. Addition of Vectors • vector sum

  10. Displacement and Distance • 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 –x0 The length of xis not the same as distance traveled !

  11. Average Speed and Velocity • Average 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 !

  12. Summary of Concepts • kinematics: A description of motion • position: your coordinates • displacement: x = change of position • velocity: rate of change of position • average : x/t • instantaneous: slope of x vs. t • acceleration: rate of change of velocity • average: v/t • instantaneous: slope of v vs. t

  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!

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