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1.5 Vectors and Scalars
Scalars
are quantities (including units) that give the size or magnitude of something.
Examples:
Mass = 45 kg
Length = 16.2 m
Speed = 15.0 m/s
Vectors
are objects that require both magnitude AND direction
to completely describe
them.
Examples:
Displacement = 10 m, 20
o
N of E
Velocity = 25 m/s, 35
o
above the horizontal
Vectors are usually represented as arrows. The arrow points along the direction of the
vector, and the length of the vector arrow is proportional to its magnitude.
Remember
→
Vectors have direction, scalars do not!
In the book, the vectors are represented in bold face. In class and on homework,
quizzes, etc., you should represent them with an arrow above the quantity.
T
→
For example, a tension force:
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Represent a position vector r that is 10 m in length and directed at
20
o
N of E.
→
N
r
→
Vectors are extremely important!!! They occur
verywhere in physics
Many objects are in motion
W
E
20
o
everywhere in physics. Many objects are in motion,
moving in all directions!!!
S
.6 Vector Addition and Subtraction
1.6 Vector Addition and Subtraction
The simplest situation occurs when the vectors are
collinear
, i.e. they lie along the
same direction.
Example
: A car moves due east with a displacement vector A = 275 m. It then
continues to move due east with a displacement vector B = 125 m. What is the total
displacement vector, R, of the car?
→
What we want to find is R = A + B.
→
→
→
N
E
A = 275 m
B = 125 m
R
= 275 m due east + 125 m due east = 400 m due east
→
R = 400 m
When
adding
two vectors, always place the tail of the second vector on the head of the
first.
What if the two vectors to be added are not collinear???
Example
: A car first moves with a displacement vector A = 275 m due east. It
then moves with a displacement vector B = 125 m at 55
o
N of W. What is the
total displacement of the car? i.e. what is R = A + B.
→
→
→
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Since these vectors are head to tail, the resultant vector is
drawn from the origin to the head of the second vector.
First, how do I find the magnitude of
R
, i.e. its length?
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This note was uploaded on 08/04/2009 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics, Mass

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