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CONVERSIONS ~
CONSTANTS ~ CHARACTERS |
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NOTE: These are the
U.S. customary (avoirdupois) equivalents, the troy or apothecary
system of equivalents, which differ markedly, was used long ago by
pharmacists |
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RULE OF THUMB FOR ESTIMATING DISTANCE TO LIGHTNING /
EXPLOSION:
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km - Divide 3 into the number of seconds which have elapsed
between seeing the flash and hearing the noise.
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miles - Multiply
0.2 times the number of seconds which have elapsed between seeing the
flash and hearing the noise.
Note: Sound vibrations cause a change of density and pressure within a
media, while electromagnetic waves do not. An audio tone won't travel
through a vacuum but can travel at 1100 ft/sec through air. When picked up
by a microphone and used to modulate an EM signal, the modulation will
travel at the speed of light. |
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| THE SPEED OF LIGHT
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| ACTUAL VALUE
| UNITS
| RULE OF THUMB
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| 2.9979246 x 10 8
| m/sec
| 3 x 10 8
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| 299.79
| m/usec
| 300
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| 3.27857 x 10 8
| yd/sec
| 3.28 x 10 8
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| 5.8275 x 10 8
| NM/hr
| 5.8 x 10 8
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| 1.61875 x 10 5
| NM/sec
| 1.62 x 10 5
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| 9.8357105 x 10 8
| ft/sec
| 1 x 10 9
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| 9.8357105 x 10 2
| ft/usec
| 1 x 10 3 | |
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SPEED OF LIGHT IN VARIOUS MEDIUMS
The speed of EM radiation through a substance
such as cables is defined by the following formula:
V = c / (u r e r) 1/2
Where: u r = relative permeability and e r = relative
permittivity The real component of e r = dielectric constant of
medium. EM propagation speed in a typical cable might be 65-90% of the speed
of light in a vacuum.
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* The speed remains constant until 82,000 ft, when it increases linearly to
1215 km/hr (755 mph, 656 kts) at 154,000 ft. Also see Mach number section for
discussion of Calibrated Air Speed (CAS) and True Airspeed (TAS) and a plot of
the speed of sound vs altitude.
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| SPEED OF SOUND IN VARIOUS MEDIUMS
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| SUBSTANCE
| SPEED (ft/sec)
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| Vacuum
| Zero
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| Air
| 1,100
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| Fresh Water
| 4,700
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| Salt Water
| 4,900
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| Glass
| 14,800
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| Steel
| 20,000 |
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FUNDAMENTAL PHYSICAL CONSTANTS
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PHYSICAL CONSTANT
| QUOTED VALUE
| S*
| SI UNIT
| SYMBOL
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| Avogadro constant
| 6.0221367 x 10 23
| 36 |
mol -1 |
NA
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| Bohr magneton |
9.2740154 x 10 -24
| 31 |
JT -1
| u B
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| Boltzmann constant
| 1.380658 x 10 -23
| 12
| JK -1
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k(=R N A)
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| Electron charge
| 1.602177 33 x 10 -19 |
49
| C
| -e |
| Electron specific charge |
-1.758819 62 x 10 11 |
53 | Ckg -1
| -e/m e
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| Electron rest mass
| 9.1093897 x 10 -31 |
54
| kg |
m e |
| Faraday constant
| 9.6485309 x 104 |
29 | Cmol-1 |
F |
| Gravity (Standard Acceleration) |
9.80665 or 32.174
| 14 |
m/sec 2 or ft/sec 2
| g
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Josephson frequency to voltage ratio
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4.8359767 x 1014
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HzV -1
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2e/h
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Magnetic flux quantum |
2.06783461 x 10 -15
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61
| Wb | Phio |
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Molar gas constant |
8.314510 |
70 | Jmol -1 K -1
| R
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Natural logarithm base |
2.71828 |
-
| dimensionless
| e |
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Newtonian gravitational constant
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6.67259 x 10 -11
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85
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m 3 kg -1 s -2
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or K
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Permeability of vacuum |
4pi x 10 -7 |
d | H/m | u o |
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Permittivity of vacuum |
8.8541878 x 10 -12 |
d | F/m | e o |
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Pi
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3.141592654 |
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dimensionless
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Pi
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Planck constant
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6.62659 x 10 -34 |
40 | Js | h |
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Planck constant/2 |
1.05457266 x 10 -34 |
63 | Js |
h(=h2) |
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Quantum of circulation |
3.63694807 x 10 -4 |
33 | Jskg -1 | h/2m e |
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Radius of earth (Equatorial) |
6.378 x 10 6 or 3963 |
- - | m or miles | - - |
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Rydberg constant |
1.0973731534 x 10 7 |
13 | m -1 | R x |
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Speed of light |
2.9979246 x 10 8 |
1 | ms -1 | c |
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Speed of sound (dry air @ std press & temp)
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331.4
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- | ms-1 | - |
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Standard volume of ideal gas |
22.41410 x 10 -3 |
19 | m 3mol -1 | V m |
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Stefan-Boltzmann constant |
5.67051 x 10 -8 |
19 |
WK -4 m -2 |
sigma |
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* S is the one-standard-deviation uncertainty in the
last units of the value, d is a defined value. (A standard deviation is the
square root of the mean of the sum of the squares of the possible deviations)
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DECIMAL / BINARY / HEX CONVERSION TABLE
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| Decimal
| Binary
| Hex
| Decimal
| Binary
| Hex
| Decimal
| Binary
| Hex
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| 1
| 00001
| 01h
| 11
| 01011
| 0Bh
| 21
| 10101
| 15h
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| 2
| 00010
| 02h
| 12
| 01100
| 0Ch
| 22
| 10110
| 16h
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| 3
| 00011
| 03h
| 13
| 01101
| 0Dh
| 23
| 10111
| 17h
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| 4
| 00100
| 04h
| 14
| 01110
| 0Eh
| 24
| 11000
| 18h
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| 5
| 00101
| 05h
| 15
| 01111
| 0Fh
| 25
| 11001
| 19h
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| 6
| 00110
| 06h
| 16
| 10000
| 10h
| 26
| 11010
| 1Ah
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| 7
| 00111
| 07h
| 17
| 10001
| 11h
| 27
| 11011
| 1Bh
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| 8
| 01000
| 08h
| 18
| 10010
| 12h
| 28
| 11100
| 1Ch
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| 9
| 01001
| 09h
| 19
| 10011
| 13h
| 29
| 11101
| 1Dh
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| 10
| 01010
| 0Ah
| 20
| 10100
| 14h
| 30
| 11110
| 1Eh |
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When using hex numbers it is always a good idea to use "h" as a suffix to
avoid confusion with decimal numbers.
To convert a decimal number above 16 to hex, divide the number by
16, then record the integer resultant and the remainder. Convert the remainder
to hex and write this down - this will become the far right digit of the final
hex number. Divide the integer you obtained by 16, and again record the new
integer result and new remainder. Convert the remainder to hex and write it just
to the left of the first decoded number. Keep repeating this process until
dividing results in only a remainder. This remainder will become the left-most
character in the hex number (after converting to hex of course).
For example, to convert 60 (decimal) to hex, we have 60/16=3 with 12
remainder. 12 is C (hex) - this becomes the right-most character. Then 3/16=0
with 3 remainder. 3 is also 3 (hex). This becomes the next (and final) character
to the left in the hex number, so the answer is 3C h.
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BASIC MATH / GEOMETRY REVIEW
A radian is the
angular measurement of an arc which has an arc length equal to the
radius of the given circle, therefore there are 2
radians in a circle.
One radian = 360° /2 = 57.296....°
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