Fundamental Physics
Table of contents
1. Units ……………………………………………………………………………………
2-4
2. Unit conversions ………………………………………………………………………
4-6
3. Scientific notation ………………………………………………………………………
7
4. Significant figures ………………………………………………………………………
7-11
5. Order of magnitude ……………………………………………………………………… 11
6. Vectors and scalars ……………………………………………………………………… 11-13
7. Direction in physics ……………………………………………………………………… 13
Done by: Mu’taz Rababah
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1. Units
In physics we are using units to describe the magnitude of a certain quantity. So, they are like
identities for the magnitudes that give us information about the quantity that we are
measuring.
Most of the physical quantities (measurements) can be expressed as a magnitude with a unit
and sometimes a direction as well.
It is very important to mention that some physical quantities are unitless which means have no
unit, like efficiency, magnification, and index of refraction.
Examples of physical quantities,
22m2 ,
-30°C
, (3N, Left)
As seen before, the unit associated with the first magnitude give us an idea that the quantity
measured in this case refers to an area while the last one refers to a force with its direction.
Generally, the magnitude represents an absolute numerical value. Which means, it can’t be
negative at all. If so, then the negative sign added to the magnitude that time represents either
a direction or a physical meaning like decreasing.
So,
A certain physical quantity = an absolute numerical value x a unit, (with direction added
sometimes)
Magnitude can never ever be a negative.
Test your understanding
Example 1: Which one of the following represents a certain physical quantity?
A. 22, left
B. Ahmad cm
C. Sec
D. 61.3+cm, down
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Scientists have classified units into three categories, as follows,
1. Basic units.
They are fundamental units from which other units may be derive. Based on the international
system of units (SI) which is commonly known as the metric system is a system that used
universally as a standard for measurements, there are only seven basic units. As follows,
Physical quantity
Name of unit
Abbreviation
Mass
Length
Time
Temperature
Electric current
Amount of substance
Luminous intensity
Kilogram
Meter
Second
Kelvin
Ampere
Mole
Candela
Kg
m
s
K
A
mol
cd
Despite the fact that Kg is derived from g but for certain reasons the international system of
units has chosen it to be the basic unit in line with the definition of the basic units.
It is worth to mention that there are other systems of units with different basic units like, C.G.S.
system (or French system) and F.P.S. system (or British system).
2. Standard units.
They are units that most of the scientists in a certain country or region agreed to use.
Example:
In gulf countries scientists agreed to use Kg to measure the mass while British’s scientists
agreed to used pound to measure the mass.
3. Derived units
As mentioned before, derived units are originally obtained from the basic units. As example,
Newton is a derived unit used to measure the force, which is equivalent to (Kg.m/s2).
Joule(J) is a derived unit used to measure the work done, which is equivalent to (Kg.m2/s2).
Test your understanding
Example 2: Which one of the following represents two basic units and one derived unit.
A. Kelvin, Watt, meter
B. Kilogram, Second, Ampere
C. Joule, Ohm, Volt
D. Tesla, Newton, Candela
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Example 3: The unit Watt is equivalent to. [Hint: 𝑃𝑜𝑤𝑒𝑟 =
A. Kg.m2/s
B. Kg/m2.s3
C. Kg.m3/s2
D. Kg.m2/s3
Example 4: The unit (
A. Tesla
B. Volt
C. Ohm
D. Weber
𝐾𝑔 . 𝑚
𝐴 . 𝑠3
𝐸𝑛𝑟𝑔𝑦
𝑡𝑖𝑚𝑒
]
) is called:
2. Unit conversions
Some units are too large or small to precisely and accurately describe a certain measurement.
This is why we sometimes need to convert them to other forms.
Units can be converted only if they have the same nature. That means we can’t convert meter
to milli second instead we do convert meter to milli meter.
To convert units, we mainly multiply or divide by the mathematical meaning of the prefix/es
included in a certain conversion.
Prefixes are letters that can be added before the basic units to make them smaller or larger.
The table below shows the most important prefixes that we frequently use along with its
mathematical meaning.
Prefix
Symbol
Value (Mathematical meaning)
Giga
Mega
Kilo
Deci
Centi
Milli
Micro
Nano
Pico
G
M
K
d
c
m
μ
n
p
109
106
103
10-1
10-2
10-3
10-6
10-9
10-12
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Unit conversions rules:
1. If the prefix was to the left side of the conversion, we just multiply by its mathematical
meaning on the other side.
Example: Convert 3 cm (Left side) to m (Right side)
3 𝑐𝑚 = 3 × 10−2 𝑚 (Left side to Right side)
As seen before, the prefix Centi is located on the left side of the conversion. So, we only
multiply by its mathematical meaning in the other side.
2. If the prefix was to the right side of the conversion, we just divide by its mathematical
meaning on the other side.
Example: Convert 5 m (Left side) to cm (Right side)
5
5 𝑚 = −2 𝑚 = 5 × 102 𝑚
10
As seen before, the prefix Centi is located on the right side of the conversion. So, we only divide
by its mathematical meaning on the other side.
3. If there are prefixes on both sides, we just apply the first two rules in one time. So, we
multiply and divide the number on the right side of the conversion by the mathematical
meaning of each prefix with respect to its position.
Example: Convert 4 Mm (Left side) to pm (Right side)
4 × 106
4 𝑀𝑚 =
𝑝𝑚 = 4 × 1018 𝑝𝑚
10−12
As seen before, the prefix Mega is located on the left side of the conversion. So, we only
multiply by its mathematical meaning on the other side. At the same time, the prefix Pico
located on the right side. So, we divide by its meaning. (All in one step)
Test your understanding
Example 5: Convert the following measurements as indicated:
a. 8 mg to g
c. 56.3 Gm to cm
b. 120 s to Ms
d. 40 dg to g
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e. 98.6x 10-2 mm to nm
It is worth to mention that some other units like time or temperature have special rules of
conversing. As shown below,
Time,
As we go from left to right,
𝑌𝑒𝑎𝑟 → 𝐷𝑎𝑦 → 𝐻𝑜𝑢𝑟 → 𝑀𝑖𝑛𝑢𝑡𝑒 → 𝑆𝑒𝑐𝑜𝑛𝑑
× 365
× 24
× 60
× 60
Oppositly, as we go from right to left, we divide instead of multiply.
Temperature,
From Celsius to Kelvin
K = °C + 273
From Celsius to Fahrenheit
°F =
9
°C + 32
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From Fahrenheit to Kelvin
K=
5
(°F − 32) + 273
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Test your understanding
Example 6: Convert the following as indicated.
a. 12x 104 hour to min
d. 23 °C to K
b. 3688 s to hour
e. 65 °F to K
c. 2 years to sec
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3. Scientific Notation
Simply, it is a way to write very large numbers or very small numbers. So, instead of writing
3300000000 as it is we can express it in scientific notation as 3.3 x 109.
The proper format of any number in scientific notation is:
𝐚 × 𝟏𝟎𝐛
where, (a) is a number between 0-9 and (b) is an integer. In case a= decimal, then it is
preferable to keep only one digit after the decimal.
Test your understanding
Example 7: Write the following in scientific notation.
a. 45768
d. 3200000
b. 0.0987
e. 498.6 x 102
c. 0.0000091
4. Significant figures
They are the digits of a number that are meaningful in terms of accuracy or precision.
The number of significant figures in a certain numerical value can be determined throughout
the following rules.
1. non-zero numbers from 1 to 9 are all significant.
Example: 98578
2. Zeros between are significant.
Example: 65009
3. Leading zeros (zeros to the left of a number) are not significant.
Example: 0.0005
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4. Trailing zeros (zeros to the right of a number) are:
a. Significant if there is a decimal.
Example: 39.20
b. Not significant if there is no decimal.
Example: 3920
Test your understanding
Example 8: How many significant figures are there in the following measurements?
a. 3784 cm
e. 0.12 V
b. 175.0 kg
f. 1004 sec
c. 456000 J
g. 6 x 109 dm
d. 3.76 x 109 mm
Rounding to a certain number of significant figures
Sometimes it is asked to have a measurement rounded to a certain number of significant
figures. In this case we have to use the following rule.
From left to right, count the number of significant figures you have to round to and then have a
look at the digit after. If it was,
1. more than 5 then round.
2. less than 5 cancel it.
3. equals to 5 and followed by only zeros or not followed by any digits. Then have a look at
the digit before. If it was,
a. odd, then round even it is less than 5.
b. even, then cancel even it is more than 5.
4. equals to 5 and followed by digit/s other than zero. Then we round.
Important note:
In all cases, if the measurement includes a decimal, then after rounding or cancelling a digit, we
have to replace it by zero. Oppositely, if the measurement was a whole number (without
decimal) then we cancel or round it without replacing it by zero. In addition, all digits followed
the digit rounded have to be replaced by zeros if the measurement doesn’t include decimal.
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Test your understanding
Example 9: Round the measurement (23.350 cm) to 3 significant figures.
After rounding the number becomes: 23.40 cm
Note that, since 5 is followed by zero and the number before it is odd, we rounded and then
replacing 5 by zero based on the rule.
Example 10: Round the following measurements as indicated.
a. (398765 mm) to 3 S.F
b. (0.0334 cm) to 1 S.F
c. (565.5 kg) to 2 S.F
Operations with significant figures.
1. Adding or subtracting significant figures. (Adding or subtracting measurements in physics)
In case of adding or subtracting significant figures, we have to write the final answer rounded to
the least decimal places among all of the measurements added or subtracted.
Example: Add the following measurements.
3.589 cm, 4.2 cm, 670.10 cm
As we can see, the least d.p among all measurements is 1 d.p. So, we have to write the final
answer as it rounded to only one decimal place. The final answer is then,
3.589 + 4.2 + 670.10 = 677.889 cm ≈ 677.9 cm
Test your understanding
Example 11: Solve the following problems and report answers with appropriate number of
significant figures.
a. 6.201 cm + 7.4 cm + 0.68 cm +12.0 cm =
9
b. 1.6 km + 1.62 m +1200 cm =
c. 8.264 g - 7.8 g =
d. 10.4168 m - 6.0 m =
e. 12.00 kg+15.001 kg=
2. Multiplying or dividing significant figures. (Multiplying or dividing measurements in physics)
In case of multiplying or dividing significant figures, we have to write the final answer rounded
to the least number of significant figures among all measurements multiplied or divided.
Example: Multiply the following measurements.
23 m , 578 m
As we can see, the least number of significant figures among all measurements is 2. So, the final
answer must be rounded to only two significant figures. The final answer is then,
23 m x 578 m = 13294 m2 ≈ 13000 m2
Test your understanding
Example 12: Solve the following problems and report answers with appropriate number of
significant figures.
a. 1.31 cm x 2.3 cm =
c. 20.2 cm / 7.4107 s =
b. 5.7621 m x 6.201 m =
d. 40.002 g / 13.000005 g =
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Example 13: Solve the following problem and report the answer with appropriate number of
significant figures.
(12.4 cm x 2.0 cm) + 1.11 cm2 =
5. Order of magnitude
Order of magnitude is usually written as 10 to the nth power. Where, n represents the order of
magnitude.
Example: state the order of magnitude of the following measurement (6.23 x10 9 m).
First, we have to write the measurement in the form of 10 to the nth power and then state the
order of magnitude.
6.23 x109 ≈ 1010 m So, the order of magnitude is 10.
Since, 6 is more than 5. So, we have to round it up directly to 10. If the first digit to the left was
less than 5 then we cancel it.
Test your understanding
Example 14: state the order of magnitude of the following measurements.
a. 7782 Kg
b. 0.4572 dm
c. 2.34 x10-5 A
6. Vectors and scalars
A scalar quantity is a quantity that requires only magnitude without direction to be described.
Example: 22 m
A vector quantity is a quantity that requires both magnitude and direction to be fully described.
34 m, left
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It is worth to mention that sometimes the direction of a vector quantity is replaced by a
negative sign that indicates it. As example 3 m, down can be written as -3 m.
Be careful, we can’t write a quantity with both negative sign and direction. This is meaningless
and totally wrong. As example -3 m, down.
Test your understanding
Example 15: Which one of the following is a vector quantity?
A. 3 J
B. -4 °C
C. 50 N, down
D. Into the page
The table below shows the most familiar vector and scalar quantities in physics.
Vector quantities
Scalar quantities
Position
Displacement
Velocity
Acceleration
Force
Distance
Speed
Time
Mass
density
Volume
Energy
Work
efficiency
Resistance
Current
Index of refraction
Power
Magnification
Potential difference
Frequency
Wavelength
Magnetic flux
Pressure
Area (Its direction represented by the normal of the area)
Field
Torque
Impulse
Momentum
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Test your understanding
Example 16: Which one of the following consists of 2 vector quantities and 1 scalar quantity?
A. momentum, force, velocity
B. time, acceleration, current
C. speed, torque. displacement
D. power, frequency, area
7. Directions in physics
In physics. Specifically in two dimensions, we can represent the direction of a certain vector
quantity by one of the following ways:
1. Left, Right, Up, Down
2. North, South, East, West
3. x-, x+, y-, y+
4. using the angle that the vector makes with a certain axis. Usually, we use “θ” to describe the
angle that the vector makes anticlockwise with x+.
The following diagram represents the directions used mainly in physics.
Up, North or y+
𝐴⃗
Left, West or x-
θ
Right, East or x+
Down, South or y-
These directions might be slightly changed based on your point of view.
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