Transcript ppt - Alvin ISD

Scalar Quantities
• Scalar quantities are measurements that
have only magnitude (size) but no
direction.
• Examples of scalar quantities are;
Distance
Speed
Temperature
Vector Quantities
• Vector quantities are measurements which
have both magnitude (size) and direction.
• Examples of vector quantities are;
Displacement
Velocity
Acceleration
Force
Displacement (a vector) vs.
Distance (a scalar)
• If you leave your driveway and run a
bunch of errands and then return and park
in the same spot, what is you distance and
what is your displacement?
• Your distance was recorded on your
odometer. Let’s say it is 10 miles.
• Your displacement is the distance from
where you started to where you finished.
In this case it is zero miles.
Speed vs. Velocity
• Speed and velocity are used
interchangeably but they are not the same
thing.
• Speed is only how fast you are going with
no direction.
• Velocity is how fast you are going and in
what direction.
Coordinate Systems
• You need to remember the X-Y coordinate
system into which a graph is divided into
four quarters by a vertical and horizontal
lines.
• Each quadrant contains 90o and if you add
all four quadrants you get 360o (a full
circle).
Up = +
Down = -
Right = +
Left = -
Rectangular Coordinates
90 o North
y
Quadrant II +
Quadrant I
West 180
o
-
o
x 0 East
360 o
Quadrant IV
+
Quadrant III
-
270 o South
Coordinate Systems
• Note: That there are multiple ways of
indicating each direction.
East or Right which is +
West or Left which is –
North or Upward which is +
South or Downward which is –
• Also note that the measure of degrees
starts at the East line and moves
counterclockwise around the graph.
VECTOR NOTATIONS
90O North
+y
-45O or
45O SOUTH OF EAST
315O
West
180O
+10 +x
-x
0O East
360O
-10
-y
270O South
Polar Form Example
• Polar Form: You find the magnitude of the
new vector line by measuring the length
on the graph.
• For our example this gives;
c = 14.1
Polar Form Example
• The angle can be determined using the
graph.
• Angle = 315o or 45o South of East
Adding Vectors Graphically
• Suppose you have two people pushing on
a box. If they are pushing on the same
side with an equal force, you can add the
two forces together to get the total force
on the box.
Adding Vectors Graphically
• Suppose now these two people are
pushing on an object that is irregular in
shape. One might be pushing a little to
the left and the other a little to the right.
Determining the total force has become
more difficult since the two people are
pushing against each other at the same
time that they are pushing against the
object.
Adding Vectors Graphically
• One method of figuring out the force (or a
number of other factors) is to add the two
vectors representing these forces
graphically.
Adding Vectors Graphically
• You assign each inch or centimeter or
some other measurement the value of 100
mph. Then you draw a line 5 inches in
one direction and 3 inches in the other.
Adding Vectors Graphically
• The solution (called the resultant) is
determined by drawing a new line from the
tail of the first vector to the head of the
second vector.
Adding Vectors Graphically
• As the bottom illustration shows you can
repeat this process for any number of
vectors. Each must be drawn to scale and
oriented in the correct direction.
• Note that you can graphically add two
vectors that are not perpendicular (at a
right angle of 90o) graphically easier than
doing it mathematically.
Adding Vectors Graphically
• Once the resultant is drawn, you measure
the length of the resultant and translate
that into you answer using the scale that
you set up to draw the vectors you are
adding.
Adding Vectors Graphically
• However, with a vector you need a
direction as well as a magnitude.
• You measure the direction of the resultant
line using a protractor. You report the
angle, you reference the angle to one of
the for axis (North, South, East or West).
Adding Vectors Graphically
• Example: You have two vectors. One is
12 N of force acting at 20o North of East.
The second is 25 N acting at 30o East of
North. What is the resultant force?
Adding Vectors Graphically