MATH SKILLS
FOR PHYSICS
Units / Unit systems
Scientific notation/ Significant
figures
Algebraic manipulation
Geometry / Trig identities
Graphing
Dimensional analysis
MATHEMATICS
• This unit is a review of most of the skills that are
necessary for understanding and applying physics.
A thorough review is critical.
 Basic geometry, algebra, formula rearrangement,
graphing, trigonometry, scientific notation, and
such are normally assumed for beginning physics.
 Please use this for review and preparation for
classwork.
Dimensions / Units



The raw material of science is measurement.
Every measurement is a comparison to some
standard.
Every measurement contains error
“The length of the football field is 100 yds.”
 Dimension – the physical characteristic being
measured – “length”
 Unit – we are using the “yard” which is a unit
of length in the common or “British” system.
 Measurement – How many of these units?
100 (yds)
Fundamental or basic
Dimensions

We recognize seven fundamental or basic
physical dimensions – the SI dimensions.


Know the five SI units in the table on page
958 of your text.
2 more not listed there:
Mole – amount of substance
 Candela – luminous intensity


These seven basic dimensions can be
combined to derive other physical
characteristics.
Derived Dimensions


Use of the basic dimensions (with correct units)
to describe many different physical
characteristics –
Example –
 From Houston to Austin is a measurement
of about 180 miles.
 If I cover that distance in 3 hours, I can
find my average speed as 180 miles / 3
hours = 60 mi/hr.
 I have “derived” a new measurement called
speed.


See other commonly used units (derived)
on p. 959 of your text.
Take note of the following derived units:
know the quantity measured and the
“conversion” (basic units)




Hertz
Joule
Newton
volt
Unit Table
Dimension
Mass (M)
______
SI unit(MKS)
cgs
Common (B/E) unit
_______
_______
________
s
_______
________
______
_______
_______
ft
______
_______
cm3
________
______
________
Velocity (L/T)
m/s
Dimension Map
Can you use the correct units?
Units


The SI system uses the metric system which is base
10. (Sometimes referred to as the MKS system meter, kilogram, second)
 The cgs (centimeter, gram, second) system is
more convenient for smaller quantities. That is
why it is frequently used in chemistry – you don’t
use a kilogram of a compound very often!
We use the “common” or “British” system of units.
You can’t just multiply or divide by ten to change the
size. You have to memorize the silly things:
 examples:
12 inches in 1 foot
3 feet in 1 yard
1760 yards in 1 mile
5280 feet in 1 mile
Working with units
Similar dimensions can be added or subtracted – nothing changes.
3m+3m= 6m
52 kg - 12 kg = 40 kg
.
BUT ----You cannot add or subtract different dimensions
3 m + 12 kg = no answer
You can’t add a distance to a mass – just common sense.
All dimensions can be multiplied or
divided

Similar dimensions
If multiplied then they become squared or cubed.
3 m x 3 m = 9 m2
If divided, then they cancel
6 m / 3 m = 2 (no unit – it cancels out)
Note: 6m2 / 3 m = 2 m

(only one “m” is cancelled)
Different dimensions
Multiplied: 3 m x 2 s = 6 m·s
Divided (a ratio): 88 km / 4 s = 22 km/s
CAREFUL! CAREFUL!


Even if working in the same dimension
(like mass) I cannot work in different
SIZES (this is what prefixes mean – like
kilo, milli, Mega, etc)!
THE PREFIXES MUST BE THE SAME !!!!!


5 kg – 2 kg = 3 kg All is good.
5 kg – 2 g = DISASTROUS CATASTROPHY!
Gotta be the same - so,
 OR 
5 kg - .002 kg is OK.
5000 g - 2 g is OK.
Scientific notation provides a short-hand
method for expressing very small and very
large numbers.
0.000000001  10 9
0.000001  10 6
0.001
v
 10 3
1  100
582m
5.82x102 m

0.0042s 4.20x103 s
1000  103
1,000,000  106
1,000,000,000  109
Examples:
93 000 000 mi = 9.30 x 107 mi
0.000 042 kg = 4.20 x 10-4 kg
582m
5.82x102 m
v

0.0042s 4.20x103 s
V = 1.39 x 10 5 m/s
SCIENTIFIC (EXPONENTIAL)
NOTATION



Since the metric system is base 10, this makes
multiplying and dividing easy. Exponential
notation is a shorthand for writing exceptionally
large or small values – but it is also very helpful
for controlling significant figures.
Using exponents can make the work much
easier.
Learn the metric prefixes from Table 1-3 on page
12. Study Sample Problem on p. 14
Metric prefixes are used to express very
small or very large numbers.

Learn the metric prefixes from Table 1-3
on page 12. Study Sample Problem on p.
14
PREFIX SUBSTITUTION



You MUST learn the value of each prefix.
Substitute the value for the prefix. This converts to the
base unit.
3.5 x 10-8 Tm = 3.5 x 10-8 (1012) m = 3.5 x 104 m
From there you can convert to the needed value.
3.5 x 104 m x km
=
3.5 x 101 km or 35 km
103 m
Remember your dimensional analysis techniques !!!!
Solve the problem:
Use the fact that the speed of light in a vacuum is about
3.00 x 108 m/s to determine how many kilometers a
pulse from a laser beam travels in exactly one hour.
(ans: 1.08 x 109 km)
How many meters? Easy, substitute 103 for “k”
1.08 x 109 (103) m = 1.08 x 10 12 m
or
1.08 Tm
Solve the problem:
The largest building in the world by volume is the Boeing
747 plant in Everett, Washington. It measures
approximately 0.631 km long, 1433 m wide and
7400 cm high. What is its volume in cubic meters?
(ans: 6.70 x 107 m3)
SIGNIFICANT FIGURES (SF)

Why is this concept so important in science?


Every measurement is limited in terms of accuracy.
This is due to both the instrument and human ability
to read the instrument.
The number of sig figs in a measurement includes the
figures that are certain and the first “doubtful” digit.


With a metric ruler a desk can be measured to 65.2 cm
– but not 65.0002 cm. It just ain’t that good !
The final answer must have the same number of sig
figs as the least reliable instrument.
The rules for sig figs and rounding can be found
on pages 17- 19 of the text.
Use Tables 1-4, 1-5 and 1-6 for SF rules
How many sig figs (SF) in each of the following measurements?
a. 3000 000 000 m/s
b. 25.030 oC
c. 0.006 070 K
d. 1.004 J
e. 1.305 20 MHz
Solve the problems:
Find the sum of: 756g, 37.2g, 0.83g, and 2.5g
Divide: 3.2m / 3.563 s
Multiply: 5.67 mm x p
(Ooohhh, sneaky. There’s a pi in there.)
Working With Formulas:
Many applications of physics require one to solve
and evaluate mathematical expressions called
formulas.
Consider Volume V, for example:
V = LWH
H
W
L
Applying laws of algebra, we can solve for L, W, or H:
V
L
WH
V
W 
LH
V
H
LW
Formula Rearrangement
Solve for A
Consider the following formula:
Multiply by B to solve for A:
Notice that B has moved
up to the right.
Thus, the solution for A
becomes:
A
C

B
D
BA BC

B
D
A BC

1
D
BC
A
D
Geometry and Trig Review

See pages 946 through 948 to review the
basic geometry and trig needed for this
course.
Trigonometry Review

You are expected to know the following:
Trigonometry
R
y
q
x
R2 = x2 + y2
y
sin q 
R
x
cos q 
R
y
tan q 
x
y = R sin q
x = R cos q
y = x tan q
Θ = tan-1(y/x)