Four Basic Types of Motion Pearson Education, Inc.

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1 Four Basic Types of Motion

2 Making a Motion Diagram An easy way to study motion is to make a video of a moving object. A video camera takes images at a fixed rate, typically 30 every second. Each separate image is called a frame. Shown are four frames from a video of a car going past. The car is in a somewhat different position in each frame.

3 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.

4 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.

5 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.

6 Examples of Motion Diagrams A motion diagram can show more complex motion in two dimensions. Example: Projectile Motion In this case the ball is slowing down as it rises, and speeding up as it falls.

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

So we can treat the object as if all its mass were concentrated into a single point.

8 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.

9 The Particle Model Motion Diagram in which the object is represented as a particle Motion diagram of a rocket launch

10 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. (a) is dust, (b) is ball, (c) is rocket. B. (a) is ball, (b) is dust, (c) is rocket. C. (a) is rocket, (b) is dust, (c) is ball. D. (a) is ball, (b) is rocket, (c) is dust.

11 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 (x 4, y 4 ) (12 m, 9 m) at time t s.

12 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. Ԧr The position vector is an alternative form of specifying position. It tells us the same information as before but simply in a different format. Ԧr

Sam s initial position is the vector. Vector is his position after he finishes walking.

13 Vector Addition Example: Displacement Sam is standing 50 ft east of the corner of 12 th 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.

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

15 Time Interval A stopwatch is used to measure a time interval. It s useful to consider a change in time ( t). An object may move from an initial position at time t i to a final position at time t f. t = t f - t i 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.

Average Speed, Average Velocity To quantify an object s fastness or slowness, we define a ratio: The victory goes to the runner with the highest average speed.

16 Average Speed, Average Velocity To quantify an object s fastness or slowness, we define a ratio: The victory goes to the runner with the highest average speed. 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:

17 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.

18 Example 1 - A skier starts from rest at the top of a 30 snow-covered slope and steadily speeds up as she skies to the bottom. When she reaches the bottom, she glides along a smooth, horizontal track. Create a motion diagram to represent this.

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.

19 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 during the time interval t. The quantity is the change in velocity. The rate of change of velocity is called the average acceleration: to The Audi TT accelerates from 0 to 60 mph in 6 s.

20 Tactics: Finding the Acceleration Vector

21 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.

22 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?

23 A particle undergoes an acceleration while moving from point 1 to point 2. Which of the choices shows the velocity vector as the object moves away from point 2?

25 Speeding Up or Slowing Down? When an object is speeding up, the acceleration and velocity vectors point in the same direction. When an object is slowing down, the acceleration and velocity vectors point in opposite directions. An object s velocity is constant if and only if its acceleration is zero. In the motion diagrams to the right, one object is speeding up and the other is slowing down, but they both have acceleration vectors toward the right.

26 QuickCheck 1.6 A cyclist riding at 20 mph sees a stop sign and actually comes to a complete stop in 4 s. He then, in 6 s, returns to a speed of 15 mph. Which is his motion diagram?

27 Tactics: Determining the Sign of the Position, Velocity, and Acceleration

28 Tactics: Determining the Sign of the Position, Velocity, and Acceleration

29 Tactics: Determining the Sign of the Position, Velocity, and Acceleration

30 QuickCheck 1.8 The motion diagram shows a particle that is slowing down. The sign of the position x and the sign of the velocity v x are: A. Position is positive, velocity is positive. B. Position is positive, velocity is negative. C. Position is negative, velocity is positive. D. Position is negative, velocity is negative.

31 QuickCheck 2.13 Here is a motion diagram of a car speeding up on a straight road: The sign of the acceleration a x is A. Positive. B. Negative. C. Zero.

32 QuickCheck 1.7 A ball is tossed straight up in the air. At its very highest point, the ball s acceleration vector A. Points up. B. Is zero. C. Points down.

33 Example 2 - Draw a complete motion diagram for: A roof tile falls straight down from a two-story building. It lands in a swimming pool and settles gently to the bottom.

Physics 4A Chapter 1: Concepts of Motion

Physics 4A Chapter 1: Concepts of Motion Conceptual Questions and Example Problems from Chapter 1 Conceptual Question 1.6 Determine the signs (positive, negative, or zero) of the position, velocity, and