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Fundamental Concepts of Motion: Introduction and Examples

This chapter introduces basic motion concepts such as particles, motion diagrams, speed vs. velocity, and SI units. Explore motion representations and understand the difference between speed and velocity. Dive into motion diagrams to grasp concepts with examples.

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Fundamental Concepts of Motion: Introduction and Examples

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  1. Chapter 1 Lecture

  2. Chapter 1 Concepts ofMotion Chapter Goal: To introduce the fundamental concepts of motion. Pickup PSE3e Photo from page 2, snowboarder jump. Slide 1-2

  3. Chapter 1 Preview Slide 1-3

  4. Chapter 1 Preview Slide 1-4

  5. Chapter 1 Reading Quiz Slide 1-5

  6. Reading Question 1.1 What is a “particle?” • Any part of an atom. • An object that can be represented as a mass at a single point in space. • A part of a whole. • An object that can be represented as a single point in time. • An object that has no top or bottom, no front or back. Slide 1-6

  7. Reading Question 1.1 What is a “particle?” • Any part of an atom. • An object that can be represented as a mass at a single point in space. • A part of a whole. • An object that can be represented as a single point in time. • An object that has no top or bottom, no front or back. Slide 1-7

  8. Reading Question 1.2 What quantities are shown on a complete motion diagram? • The position of the object in each frame of the film, shown as a dot. • The average velocity vectors (found by connecting each dot in the motion diagram to the next with a vector arrow). • The average acceleration vectors (with one acceleration vector linking each two velocity vectors). • All of the above. Slide 1-8

  9. Reading Question 1.2 What quantities are shown on a complete motion diagram? • The position of the object in each frame of the film, shown as a dot. • The average velocity vectors (found by connecting each dot in the motion diagram to the next with a vector arrow). • The average acceleration vectors (with one acceleration vector linking each two velocity vectors). • All of the above. Slide 1-9

  10. Reading Question 1.3 In physics, what is the difference between “speed” and “velocity”? • Velocity is represented by an exact number, while speed is only an approximate number. • Speed can be positive or negative, while velocity is always positive. • Speed is a scalar, which is the magnitude of the velocity, which is a vector. • Velocity is a scalar and speed is a vector. • Speed and velocity mean the same thing. Slide 1-10

  11. Reading Question 1.3 In physics, what is the difference between “speed” and “velocity”? • Velocity is represented by an exact number, while speed is only an approximate number. • Speed can be positive or negative, while velocity is always positive. • Speed is a scalar, which is the magnitude of the velocity, which is a vector. • Velocity is a scalar and speed is a vector. • Speed and velocity mean the same thing. Slide 1-11

  12. Reading Question 1.4 An acceleration vector • Tells you how fast an object is going. • Is constructed from two velocity vectors. • Is the second derivative of the position. • Is parallel or opposite to the velocity vector. • Acceleration vectors weren’t discussed in this chapter. Slide 1-12

  13. Reading Question 1.4 An acceleration vector • Tells you how fast an object is going. • Is constructed from two velocity vectors. • Is the second derivative of the position. • Is parallel or opposite to the velocity vector. • Acceleration vectors weren’t discussed in this chapter. Slide 1-13

  14. Reading Question 1.5 The pictorial representation of a physics problem consists of • A sketch. • A coordinate system. • Symbols. • A table of values. • All of the above. Slide 1-14

  15. Reading Question 1.5 The pictorial representation of a physics problem consists of • A sketch. • A coordinate system. • Symbols. • A table of values. • All of the above. Slide 1-15

  16. Reading Question 1.6 The basic SI units are • Second, meter, gram. • Second, meter, kilogram. • Second, centimeter, gram. • Meter, meter/second, meter/second2. • Yard, span, cubit. Slide 1-16

  17. Reading Question 1.6 The basic SI units are • Second, meter, gram. • Second, meter, kilogram. • Second, centimeter, gram. • Meter, meter/second, meter/second2. • Yard, span, cubit. Slide 1-17

  18. Chapter 1 Content, Examples, and QuickCheck Questions Slide 1-18

  19. Four basic types of motion Slide 1-19

  20. Making a Motion Diagram • Consider a movie of a moving object. • A movie camera takes photographs at a fixed rate (i.e., 30 photographs every second). • Each separate photo is called a frame. • The car is in a different position in each frame. • Shown are four frames in a filmstrip. Slide 1-20

  21. Making a Motion Diagram • Cut individual frames of the filmstrip apart. • Stack them on top of each other. • This composite photo shows an object’s position at several equally spaced instants of time. • This is called a motion diagram. Slide 1-21

  22. Examples of Motion Diagrams • An object that has a single position in a motion diagram is at rest. • Example: A stationary ball on the ground. • An object with images that are equally spaced is moving with constant speed. • Example: A skateboarder rolling down the sidewalk. Slide 1-22

  23. Examples of Motion Diagrams • An object with images that have increasing distance between them is speeding up. • Example: A sprinter starting the 100 meter dash. • An object with images that have decreasing distance between them is slowing down. • Example: A car stopping for a red light. Slide 1-23

  24. Examples of Motion Diagrams • A motion diagram can show more complex motion in two dimensions. • Example: A jump shot from center court. • In this case the ball is slowing down as it rises, and speeding up as it falls. Slide 1-24

  25. QuickCheck 1.1 Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is going slower? Car A Car B Slide 1-25

  26. QuickCheck 1.1 Motion diagrams are made of two cars. Both have the same time interval between photos. Which car, A or B, is going slower? Car A Car B Slide 1-26

  27. The Particle Model • Often motion of the object as a whole is not influenced by details of the object’s size and shape. • We only need to keep track of a single point on the object. • So we can treat the object as if all its mass were concentrated into a single point. • A mass at a single point in space is called a particle. • Particles have no size, no shape and no top, bottom, front or back. • Below is a motion diagram of a car stopping, using the particle model. Slide 1-27

  28. The Particle Model Motion Diagram in which the object is represented as a particle Motion diagram of a rocket launch Slide 1-26

  29. QuickCheck 1.2 Three motion diagrams are shown. Which is a dust particle settling to the floor at constant speed, which is a ball dropped from the roof of a building, and which is a descending rocket slowing to make a soft landing on Mars? • (a) is dust, (b) is ball, (c) is rocket. • (a) is ball, (b) is dust, (c) is rocket. • (a) is rocket, (b) is dust, (c) is ball. • (a) is rocket, (b) is ball, (c) is dust. • (a) is ball, (b) is rocket, (c) is dust. Slide 1-29

  30. QuickCheck 1.2 Three motion diagrams are shown. Which is a dust particle settling to the floor at constant speed, which is a ball dropped from the roof of a building, and which is a descending rocket slowing to make a soft landing on Mars? • (a) is dust, (b) is ball, (c) is rocket. • (a) is ball, (b) is dust, (c) is rocket. • (a) is rocket, (b) is dust, (c) is ball. • (a) is rocket, (b) is ball, (c) is dust. • (a) is ball, (b) is rocket, (c) is dust. Slide 1-30

  31. Position and Time • In a motion diagram it is useful to add numbers to specify where the object is and when the object was at that position. • Shown is the motion diagram of a basketball, with 0.5 s intervals between frames. • A coordinate system has been added to show (x, y). • The frame at t 0 is frame 0, when the ball is at the origin. • The ball’s position in frame 4 can be specified with coordinates (x4, y4)  (12 m, 9 m) at time t4 2.0 s. Slide 1-31

  32. Position as a Vector • Another way to locate the ball is to draw an arrow from the origin to the point representing the ball. • You can then specify the length and direction of the arrow. • This arrow is called the position vector of the object. • The position vector is an alternative form of specifying position. • It does not tell us anything different than the coordinates (x, y). Slide 1-32

  33. Tactics: Vector Addition Slide 1-33

  34. Vector Addition Example: Displacement Sam is standing 50 ft east of the corner of 12th Street and Vine. He then walks northeast for 100 ft to a second point. What is Sam’s change of position? • Sam’s initial position is the vector . • Vector is his position after he finishes walking. • Sam has changed position, and a change in position is called a displacement. • His displacement is the vector labeled . Slide 1-34

  35. The negative of a vector. Definition of Displacement • The displacement of an object as it moves from an initial position to a final position is • The definition of involves vector subtraction. • With numbers, subtraction is the same as the addition of a negative number. • Similarly, with vectors Slide 1-35

  36. Tactics: Vector Subtraction Slide 1-36

  37. QuickCheck 1.3 Given vectors and , what is ? Slide 1-37

  38. Given vectors and , what is ? QuickCheck 1.3 Slide 1-38

  39. QuickCheck 1.4 Given vectors and , what is ? Slide 1-39

  40. Given vectors and , what is ? QuickCheck 1.4 Slide 1-40

  41. Time Interval • It’s useful to consider a change in time. • An object may move from an initial position at timeti to a final position at time tf. • Different observers may choose different coordinate systems and different clocks, however, all observers find the same values for the displacement  and the time interval t. A stopwatch is used to measure a time interval. Slide 1-41

  42. Average Speed, Average Velocity To quantify an object’s fastness or slowness, we define a ratio: • Average speed does not include information about direction of motion. • The average velocity of an object during a time interval t, in which the object undergoes a displacement  , is the vector: The victory goes to the runner with the highest average speed. Slide 1-42

  43. Motion Diagrams with Velocity Vectors • The velocity vector is in the same direction as the displacement  . • The length of is directly proportional to the length of  . • Consequently, we may label the vectors connecting the dots on a motion diagram as velocity vectors . • Below is a motion diagram for a tortoise racing a hare. • The arrows are average velocity vectors. • The length of each arrow represents the average speed. Slide 1-43

  44. EXAMPLE 1.2 Accelerating Up a Hill Motion diagram of a car accelerating up a hill. Slide 1-44

  45. Acceleration • Sometimes an object’s velocity is constant as it moves. • More often, an object’s velocity changes as it moves. • Acceleration describes a change in velocity. • Consider an object whose velocity changes from to during the time interval ∆t. • The quantity is the change in velocity. • The rate of change of velocity is called the average acceleration: The Audi TT accelerates from 0 to 60 mph in 6 s. Slide 1-45

  46. Tactics: Finding the Acceleration Vector Slide 1-46

  47. Tactics: Finding the Acceleration Vector • Notice that the acceleration vectors goes beside the dots, not beside the velocity vectors. • That is because each acceleration vector is the difference between two velocity vectors on either side of a dot. Slide 1-47

  48. QuickCheck 1.5 A particle has velocity as it accelerates from 1 to 2. What is its velocity vector as it moves away from point 2 on its way to point 3? Slide 1-48

  49. QuickCheck 1.5 A particle has velocity as it accelerates from 1 to 2. What is its velocity vector as it moves away from point 2 on its way to point 3? Slide 1-49

  50. The Complete Motion Diagram Slide 1-50

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