Ch 3 Describing Motion

1
Ch 3 Describing Motion

• How do you know if something moves if you dont
  see it?

2
Picturing Motion

• An object in motion changes its POSITION relative
  to some frame of reference.
• Motion diagrams help us study motion.
• A camcorder records an image 30x per sec. Each
  image is a FRAME. What do consecutive frames
  look like?

3

• A MOTION diagram helps study the position changes
  of an image while the surroundings stay put.
• At rest constant speed
• Speeding up slowing down

4
Operational Definitions

• Defining a concept in terms of the procedure or
  operation used to define it
• If the change of positions gets LARGER, the
  jogger is SPEEDING UP.
• If the change of positions gets smaller, the
  jogger is slowing down.

5
The Particle Model

• It is easier to track motion of an object by
  replacing the object with a single point. This
  is called the Particle Model. From this central
  point you can make measurements of distance with
  relation to the point and origin.

6
Where and When?

• Deciding where to put a measuring tape and when
  to start a stopwatch is defining a coordinate
  system. The origin of the system is the zero
  point of the variables. It could be a starting
  line. It is a frame of reference. A horizontal
  line from the origin is the x axis and a vertical
  line is the y axis. A jumper might need to know
  positions in both dimensions.

7
Position Vectors

• A position vector is an arrow that locates an
  object at a particular time in an event. The
  arrow is drawn from the origin to the position of
  the object. The length of the arrow is
  proportional to the objects distance from the
  origin.

8
What about Negatives?

• Can you have a negative position? A negative
  time? YES! If the origin was to the left of the
  object and the x axis was labeled positive to the
  right of the origin, then a position to the left
  of the origin would be negative.
• Time could be negative if it took place before
  the clock was started. Both negative time and
  position are possible and acceptable.
• origin

9
Vectors and Scalars

• Scalars are numbers with a magnitude only.
  Examples include mass, time, Temperature, speed,
  distance, density, volume, etc they are
  abbreviated by letters ie t, m/s, kg, g/mL
• Vectors are numbers with magnitude and direction.
  Examples include weight, Force, velocity,
  acceleration, displacement. They are abbreviated
  with a letter and arrow over it or a bold letter
  ie v, a, F, w Vectors can be represented with a
  proportional arrow.

10
Time Intervals and Displacement

• Displacement is the distance and direction
  between an object and a frame of reference or
  another object. If you make 4 left turns, how
  does your distance covered compare with your
  displacement? ?d ?
• Time interval is the difference in time between 2
  points in an event. ?t t1 t0 where t1 is
  the ending time and t0 is the starting time. ?
  means change.

11
Velocity and Acceleration

• Average velocity is the change in position for a
  certain time interval. Thus
• ?d / ?t (d1 d0) / (t1- t0)
• Average Speed is the TOTAL DISTANCE
• TOTAL TIME
• Both measurements have standard units of m/s.
  However, only 1 measurement is a vector average
  velocity! Displacement is NOT the same as
  Distance.

12
Instantaneous Velocity

• Speed and direction of an object at a particular
  instant in time. Symbol v
• What part of your car tells you the instantaneous
  velocity?
• IF Average velocity ?d / ?t, then displacement
  v?t

13
Combining Vectors

• Use arrows to represent vectors
• 2 components ? resultant
• Resultant ? 2 components resolution
• ?
• 6m/s 4m/s 10m/s
• This is called the tail-to-head method of
  combining vectors. Just pick the arrow up and
  move it as needed. (Must maintain the same
  orientation in space)

14

• How about subtraction?
• 10 m/s - 4 m/s ?
• 6 m/s

15
Your turn to practice

• Calculate the resultant velocity of Freda Flyer
  who normally flies at 100 km/h and then
  encounters a 10-km/h headwind (wind coming from
  ahead).
• 2. Calculate Freda Flyers speed in a 10-km/h
  tailwind (wind coming from behind).

16
Vectors at angles

• Use the tail-to-head method to draw a
  parallelogram. Bisect the parallelogram with the
  Resultant vector (R).
• R
• Using Pythagorean theorem, we can solve for R.
  R2 a2 b2

17
Your turn to Practice

• 3. Calculate the resultant velocity of a pair
  100-km/h velocities at right angles to each
  other.
• 4. If two vectors of magnitude 3N and 4N are at
  right angles to each other, what is their
  resultant?