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 1 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 2 Addition of Vectors Graphical Tail to head method Resultant of Forces Addition of Vectors Physics 101 Lecture 4 Pg 3 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 4 Addition of Vectors 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 Physics 101 Lecture 4 Pg 5 Scalar Components of a Vector in 2 dim Vector components of vector A A Ax Ay Scalar components of vector A A Ax x Ay y 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 Physics 101 Lecture 4 Pg 6 Scalar Components of a Vector in 2 dim Scalar A components of vector 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 7 Addition of Vectors Using 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 By 3 Calculate C and C2 Cx 2 CY 2 Tan 1 Cy Cx Physics 101 Lecture 4 Pg 8 Addition of Vectors vector sum Physics 101 Lecture 4 Pg 9 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 x is not the same as distance traveled Physics 101 Lecture 4 Pg 10 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 Physics 101 Lecture 4 Pg 11 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 Physics 101 Lecture 4 Pg 12 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 Physics 101 Lecture 4 Pg 13
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