Representing Motion

Chapter 2 Representing Motion We will begin by studying motion in a straight line; we will eventually learn about motion in 2 dimensions (projectiles and circular motion) and vibrating objects.

2.1 Picturing Motion Motion diagram – a series of images showing the positions of a moving object at equal time intervals Particle model – simplified version of a motion diagram using dots to represent the object in motion.

Motion Diagram: shows position of a moving object at equal time intervals Particle Diagram: Simplified version of the motion diagram

Motion Diagram of Bird Bird’s Eye view Wing Tip View

Motion Diagram of a Car

The Big Race

“how much ground an object has covered” Mechanics - Study of motion Kinematics - Description of motion Dynamics - Causes of motion Terms: distance displacement velocity speed Description of motion – how fast, how long of a trip, how far words, diagrams, numbers, graphs & equations Walk 4 m S (right in 218) 8 m E, 4 m N, and 8 m W Total distance = 24 m acceleration distance - “how much ground an object has covered”

2.2 Where and When Coordinate system – system used to describe motion that gives the zero point location of the variable being studied and the direction in which the values of the variable increase. 2 4 6 8 10

Can an object have a negative position? Yes

Vectors vector – quantity that has magnitude and direction magnitude = size • Examples: velocity, acceleration, force • Arrows are used to represent vectors • The sum of two or more vectors is called the resultant

Scalars Have magnitude only Examples: mass, temperature, time

Scalar quantity any quantity that only has magnitude ( amount) Examples: scalar vector displacement distance velocity acceleration time temperature mass volume speed density

Time Interval t t = tf – ti t is used to represent time t is the change between two times t = tf – ti Usually, initial time is zero.

Displacement d d = df – di d is used to represent position d is the change between two positions d = df – di Usually, initial position is zero.

displacement includes direction change in position 2m S 3m S 5 m S displacement includes direction (vector quantity) Any quantity that includes direction to be completely described Displacement – term familiar with, but not its true meaning Example: using windows as a reference point, I am 2 m S of the window. This is my original position- I move 3 m S or to the right. My new position is 5 m S.

displacement is not the same as distance 4m S 1 m S 3m N distance = 7 m displacement = 1m S

Other directions: 5 m up +5m + 3m 3 m right 4 m left 2 m down -2m -4m Signs may also me used + Right , up, North Left, down,South -

Δd = df - di displacement = change in position = final position – initial position Δd = df - di 10 20 30 40 50 60 cm xi=20 cm xf=55 cm Δd = df - di Δd = 55.00cm – 20.00 cm or 35 cm right

10 20 30 40 50 60 cm xf=20 cm xi=45 cm or 25 cm left

Only the initial position and the final position is important. A bug travels from the 45 cm mark to the 60cm and then to the 5 cm and ends at the 20 cm mark.

Vertical displacement Dy is used instead of Dx 10 20 30 40 50 60 yf = +40 cm or 40 cm up yi

Final displacement may also be found by adding displacements (with direction included) 2 3 1 Bug travels 30 cm right, then 20 cm left and finally 10 cm right. +30 cm + (-20cm) + 10 cm = + 20 cm or 20 cm right

2.3 Position-Time Graphs Plot time data on horizontal (x) axis Plot position data on vertical (y) axis Pg 39 #9, 11 Pg 41 #14- 18

(go to “describing motion with graphs” ppt)