Vectors
And Physics
By: Mr. Recore
Overview
This Presentation will teach you
What Defines a vector quantity
Where in Physics vectors are used
How vectors are added together
This is a great video to get you started, particularly pay
attention to time 0:00:00 – 0:00:47 and 0:02:53 – 0:03:40
Click here
What defines a vector?
Vector Quantity
A vector is any quantity defined
with two attributes:
They are.
Magnitude (size)
and
Direction
Vectors are found in many
physics concepts
In Physics, we represent vectors
either with a ‘’ over the
symbol, a capitalized and bolded
symbol, or an
when
represented graphically
Examples of vectors:
X = 5m west
V = 12m/s at an angle of 30°
North of East
â = 9.8m/s2 down
Where do we use
vectors?
Vector Symbol
Vector name
Magnitude name
Direction
example
X
Displacement
Distance
West
V
Velocity
Speed
15°
A
Acceleration
Thrust
Down
F
Force
Push/Pull
Left
P
Momentum
Inertia
30° E of S
Plus Many others
Vector Addition
Done Graphically (arrows)
Arrow of vector shows to-scale magnitude and direction
Head to Tail Method
Tail of first vector (side without the arrow) matches to Head
(side with the arrow) of second vector
Vector drawn from tail of first to head of second is called the
“resultant” vector, and is the single vector that can be used
to represent both
Tail
Head
Vector Addition
Sample problem.
You have 2 people exerting a force on a box in different
directions. One person is pulling with a force of F = 15N
East (right), and the other is pulling with a Force of F =
5N North (up). What is the resultant?
Solution:
Draw the situation with both tails of the vectors at the
center point (center of mass) of the object
Vector Addition
Then move one of the vectors so that its tail touches
the others head. As so…
R
The Resultant is as shown…
Vector Addition
Using the Pythagorean Theorem we can find the
magnitude of the resultant.
If you don’t remember the Pythagorean Theorem go
here for a tutorial before moving on.
All set? Click to go to the next slide
Oops
Please go back and click the link
Vector Addition
Our two Forces were 5N and15N,
Using our Pythagorean Theorem
C2 = A2 + B2
We can find the magnitude of the resultant
R2 = 52 + 152
= 25 + 225 = 250
R =
250
= 15.8 N

Vector Addition
So, our resultant has a magnitude 15.8N
15 N
5N
R 15.8 N
And now we don’t need the other two vectors…as
shown
Determining Direction
Although we can now represent the two vectors as
one, our resultant ISN’T a vector until we give it
direction!
To do this, we need to use trigonometry of right
triangles (click for a great video)
All set? Click to move on to next slide
Oops
Please go back and click the link
Determining Direction
15 N
5N
θ
R 15.8 N
We want to find the angle
shown.
As in the video, we can use
the Inverse Tan function
and get…
You Try first…then click
mouse button
If you think you got it, click
here for the answer
If you need more help, click
here
Oops
Please go back and click the link
More Help
To find the angle, use…
θ = Tan-1( 15 N / 5 N )
15 N
5N
θ
= Tan-1 (3)
= 71.6°
And our final added vector quantity
is…Click here
R 15.8 N
Answer
15.8 N at an angle of 71.6° East of North.
Do you understand? If not go back and look at the
extra help slide again
If you do understand, tell me why this answer is also
correct
15.8 N @ 18.4° N of E
Good Job!!
You’re well on your way to understanding vectors.
Please refer back to this presentation if you need to
revisit it at any time.
References
http://www.southrange.k12.oh.us/library/dictnry.gif
http://thespacereport.org/store/images/categories/vi
deo_icon_full.jpg
http://thevitaminm.files.wordpress.com/2009/12/bowl
ofpopcorn.jpg