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7/29/2019 01 - Review of Vectors and Scalars
1/24
Review of Vectors andScalars; Scientific Notation
and Units
Ms. Mikaela Fudolig
Physics 71 EEE
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Review: Vectors and Scalars
Scalars magnitude only
Vectors magnitude and direction
Scalar representation: number + unitsVector representation
Arrows
Unit vectors
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Scalar addition
Scalar + Scalar (never Scalar + Vector)
Scalars must have the same units before
you can add them (never kg + mL)
How to add: just add arithmetically
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Vector addition: Graphical
representation
Tail-to-head
A
B
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Vector addition: Graphical
representation
Tail-to-head
A
BC
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Vector addition: Graphical
representation
Tail-to-head
A
B
C
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Scalar-Vector Multiplication
Scalar x Vector
Magnitude changes (length of arrow)
Direction:
Scalar > 0: Direction REMAINS THE SAME
Scalar < 0: Direction REVERSES
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Vector Subtraction: Graphical
representation
Similar procedure as in vector addition
Technique:
Reverse direction of the vector to be subracted:
( 1)A A
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Unit Vectors
Vectors are expressed as a combination of
unit vectors
- one vector of length 1 in the +x direction - one vector of length 1 in the +y direction
- one vector of length 1 in the +z direction
i
j
k
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Vector Addition
Add the is to the is, the js to the js, and
the ks to the ks.
Arithmetic
Do NOT add the is to the js, etc.
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Scalar-Vector Multiplication
Multiply ALL components by that scalar
. 2( 4 ) 2 8ex i j i j
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Converting from graphical to analytic
Trigonometry!
Never forget:
SOHCATOAPythagorean theorem
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Exercise 1
A vector has a length of 3 units and is
directed 30 north of west. Express this
vector in terms of the unit vectors i, j, and
k. Assume that north points in the +jdirection.
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Exercise 2
A vector has a length of 3 units and is
directed 30 west of north. Express this
vector in terms of the unit vectors i, j, and
k. Assume that north points in the +jdirection.
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Exercise 3
Consider the displacement vector:
How long is this vector, and in what
direction does it point?
3m 2 mi j
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Exercise 4
Give the resultant of the following vectors:
3m 2 mA i j
5m 2 m 3mB i j k
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Units and Scientific Notation
Units are important to know the amount of
a quantity (scalar or vector).
Meter vs. foot
Gram vs. kilogram
I weigh 100. (what?)
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Converting Units
Dimensional Analysis
Involves multiplying quantities by a factor of 1
?
5.00 1
ft
cm cm
1 15.00
? 12
in ft cm
cm in
1 15.00
2.54 12
in ft cm
cm in
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Significant figures
All nonzero digits are significant.
All zeroes between significant figures are
significant.
If a whole number ends in a zero and
there is no decimal point after it, the digit
0 is not significant. (ex. 100 vs 100.)
A 0 is significant if it is trailing, not if it is
leading (ex. 0.010)
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Scientific Notation and SF
Using scientific notation makes it easier to
identify SF
1.30 x 103 g vs. 1300g
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Exercise
How many SF are there?
100.20 m
0.01050 g
10030 cm
500.0 m
2.050 x 103 J
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Operations with SF
Addition/Subtraction
SF after the decimal place is what is important
SF post-decimal place of Sum/difference must
be the same as the post-decimal place SF ofthe addend/subtrahend with the smallest post-
decimal place SF
Ex. 100.15 + 10.2 = 110.35 110.4
expressed in scientific notation, express them
with the same exponent, then add.
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Operations with SF
Multiplication/Division
Product/Quotient must have the same SF as
the factor/divisor/dividend the smallest SF
Ex. 100 x 25.0 = 2500 3000
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Operations with SF
If you have more than one arithmetic
operation, do NOT use the SF rules to
round up or down!
Ex. 120.0 + 55 x 10 = 120.0 + 550 = 670
not 120.0 + 600
Ex. 120.0 + 55.0 x 100.0 = 1.200 x 102 + 5.50 x
102 = 6.70 x 102