PAGE EDITORS: Julia Telischi, Alix Hamilton, Jade Azari, and Phil Straus

Natland Note: (9/12/13) The video still does not work! Somebody needs to see me about this one.

Your wiki page is due by 9/06/13


NOTES:

DIMENSIONAL ANALYSIS
There are three basic types of measurements (for now).
Physical Quality
Dimensions
Base Unit
Length
[L]
meter (m)
Mass
[M]
kilogram (kg)
Time
[T]
second (s)
Other things can be measured by manipulating these dimensions.
For example:
Derived Units
Dimensions
Base Unit
Volume
[L]^3
m^3
Velocity
[L]/[T]
m/s
Acceleration
[L]/[T]^2
m/s^2

In order for an equation to be dimensionally correct, it must have the exact same dimensions on both sides.
Examples:
x = x + vt + .5at^2
L = L + (L/T)(T) + (L/T^2)(T^2)
L = L + L + L
Dimensionally Correct
(note: the coefficient .5 does not have a dimension)

v = v + 3at^2
L/T = L/T + (L/T^2)(T^2)
L/T = L/T + L
NO!

VECTORS

  • Vector quantities vs. Scalar quantities
    • scalar- a physical quantity that requires only magnitude and units to be fully defined
      • ex.- mass, time, speed, length, temperature
    • vector- a physical quantity that requires magnitude AND direction to be fully defined
      • ex.- displacement, velocity, acceleration, force
  • Identifying vectors
    • aren't vectors MARvelous? M=magnitude A=angle R=reference must be stated when identifying a vector
    • ex. A= 20m at 30 degrees West of North

external image u3l1a6.gif

external image u3l1a3.gif









COMPONENTS
  • A component literally means an ingredient or part, so naturally they are the parts that make up a vector
  • a projection of a vector onto an axis
  • If the angle with the x-axis is greater than 45 degrees, the x component will be longer than the y component
  • Can be thought of as shining a flashlight on the vector and seeing its shadow on the axis
  • The x and y components are perpendicular to each other and form a right triangle with the resultant vector
vect5.gif
external image u3l1b3.gif

ADDING & SUBTRACTING VECTORS
  • note: adding vectors is commutative but subtracting them is not
1. Parallelogram Method
  • put the two vectors being added tail-to-tail and then draw them again head-to-head to make a parallelogram
  • Draw the resultant vector from the two tails to the two heads
  • ex.2. Tail-to-head

Item Picture
Item Picture
external image addition_f13d.gif
2. Tail-to-head
  • put the vectors being added tail to head and draw the resultant vector from the tail of the first vector to the head of the last vector
  • To find the magnitude of the resultant vector,
    • break the vectors being added into x and y components using trig functions
    • add all of the x components, then all the y components
      • don't forget to subtract if the component vector goes in the negative direction
    • use pythagorean theorem to find the resultant magnitude
  • Use inverse trig functions to find the angle of the resultant vector

external image 3_manyvectors.jpg

  • note: "Vectors in the same direction can be added or subtracted by adding or subtracting their magnitudes. If you add two vectors in opposite directions, their magnitudes are subtracted, not added."


SUBTRACTING VECTORS:
  • Can be seen as adding the "negative" vector
  • The negative of a vector has the same magnitude, but is antiparallel - that is, facing exactly 180 degrees in the opposite direction
  • Either the parallelogram or the tail-to-head method can be used to calculate the resultant vector

external image 315937.image1.jpg

**Quick Review of Trig Functions:
  • useful for finding the x and y components of a vector as well as its angle
external image sctohanoa.jpg


Example showing how to correctly apply Trig Functions:

u3l3b5.gif


ORDERS OF MAGNITUDE

"Powers of Ten"
http://www.youtube.com/watch?v=0fKBhvDjuy0
Scale of the Universe


SAMPLE PROBLEMS:

external image vector_image.gif 1. What is the magnitude and direction of the vector on the left?
Answer: 2.3 units at 55 degrees North of East or 2.3 units at 35 degrees East of North

More practice on identifying vectors: http://www.mathwarehouse.com/vectors/


More practice on adding vectors: http://www.physicsclassroom.com/morehelp/vectaddn/practice.cfm
http://www.physicsclassroom.com/Class/vectors/u3l1b.cfm

More practice on adding vectors (word problems):
http://physics.info/vector-addition/problems.shtml


Practice on subtracting vectors (with video demonstrations): http://www.onlinemathlearning.com/vector-subtraction.html


external image addition_f24.gif
external image vec9a.gif
http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html#vec9

Click here to see a SAMPLE VECTOR PROBLEM walked through, including all steps (e.g. breaking into components, finding the direction of the resultant vector,etc.)












WEBSITES:




Very quick video illustrating how to use dimensional analysis to find the correct equation: https://www.youtube.com/watch?v=rLAEc0xcI2k



Vector Basics - Drawing Vectors/Vector Addition




Adding & Subtracting Vectors: https://www.youtube.com/watch?v=2dHk_yJ9ntQ&feature=player_embedded



Adding & Subtracting Vectors (part two): https://www.youtube.com/watch?v=mFu5IPOG5Cw



Introduction to Vectors:
https://www.youtube.com/watch?feature=player_embedded&v=-3E9SdgW8KU

*Note: this video describes the concept of equal vectors from 2:10-3:15 which we did not discuss in class, but the rest of the video is relevant





How to find the resultant of three or more vectors: https://www.youtube.com/watch?v=g_TnqKX5ybY












SOURCES:
http://www.physicsclassroom.com/class/vectors/u3l1a.cfm

http://www.compadre.org/introphys/items/detail.cfm?ID=7782

http://sdsu-physics.org/physics180/physics195/Topics/chapter3.html

http://zonalandeducation.com/mstm/physics/mechanics/vectors/findingComponents/findingComponents.htm

http://www.numeracy-bank.net/images/trigonometric_functions/sctohanoa.jpg

http://www.physicsclassroom.com/Class/vectors/u3l1b3.gif

http://www.physchem.co.za/vectors/graphics/addition_f13d.gif

http://www.physchem.co.za/vectors/graphics/addition_f24.gif

http://www.physicsclassroom.com/class/vectors/u3l3b.cfm