Representing Motion Chapter 2 Representing Motion We will

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’s Eye view Wing Tip View

Motion Diagram of a Car

The Big Race

Mechanics - Study of motion Kinematics - Description of motion Dynamics - Causes of motion Terms: distance speed displacement velocity 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. 0 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 distance displacement velocity acceleration time temperature mass volume speed density

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

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

displacement: change in position 2 m S 3 m S 5 m. S displacement includes direction (vector quantity) Any quantity that includes direction to be completely described

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

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

displacement = change in position = final position – initial position Δd = df - di 10 20 30 xi=20 cm Δd = df - di Δd = 55. 00 cm – 20. 00 cm or 35 cm right 40 50 60 xf=55 cm cm

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

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

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

Final displacement may also be found by adding displacements (with direction included) 0 2 3 Bug travels 30 cm right, finally 10 cm right. 1 then 20 cm left and +30 cm + (-20 cm) + 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)