PAGEEDITORS: 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

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

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

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

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

**Quick Review of Trig Functions:

useful for finding the x and y components of a vector as well as its angle

Example showing how to correctly apply Trig Functions:

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

PAGEJulia Telischi, Alix Hamilton, Jade Azari, and Phil StrausEDITORS:The video still does not work! Somebody needs to see me about this one.Natland Note: (9/12/13)Your wiki page is due by 9/06/13

NOTES:DIMENSIONAL ANALYSIS

There are three basic types of measurements (for now).

For example:

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

COMPONENTS

ADDING & SUBTRACTING VECTORS

- note: adding vectors is commutative but subtracting them is not

1. Parallelogram Methodaddtwo vectors in opposite directions, their magnitudes aresubtracted, not added."SUBTRACTING VECTORS:

antiparallel- that is, facing exactly 180 degrees in the opposite direction**Quick Review of Trig Functions:

Example showing how to correctly apply Trig Functions:

ORDERS OFMAGNITUDE"Powers of Ten"

http://www.youtube.com/watch?v=0fKBhvDjuy0

Scale of the Universe

SAMPLE PROBLEMS: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

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