SI Derived Units
Derived quantity | Name | Symbol | Other symbol | Base units |
plane angle | radian | rad | - | m·m-1 = 1 |
solid angle |
steradian | sr | - | m2·m-2=1 |
frequency | hertz | Hz | - | s-1 |
force | newton | N | - | m·kg·s-2 |
pressure, stress |
pascal | Pa | N/m2 | m-1·kg·s-2 |
energy, work, quantity of heat |
joule | J | Nm | m2·kg·s-2 |
power, radiant flux |
watt | W | J/s | m2·kg·s-3 |
electric charge, quantity of electricity |
coulomb | C | - | s·A |
electric potential, difference, electromotive force |
volt | V | W/A | m2·kg·s-3·A-1 |
capacitance | farad | F | C/V | m-2·kg-1·s4·A2 |
electric conductance |
siemens | S | A/V | m-2·kg-1·s3·A2 |
electric resistance | ohm | W | V/A | m2·kg·s-3·A-2 |
magnetic flux | weber | Wb | Vs | m2·kg·s-2·A-1 |
magnetic flux density | tesla | T | Wb/m2 | kg·s-2·A-1 |
inductance | henry | H | Wb/A | m2·kg·s-2·A-2 |
Celsius temperature | degree Celsius | °C | - | K |
luminous flux | lumen | lm | cd·sr | m2·m-2·cd = cd |
illuminance | lux | lx | lm/m2 | m2·m-4·cd = m-2·cd |
activity (of a radionuclide) | becquerel | Bq | - | s-1 |
absorbed dose, specific energy (imparted), kerma | gray | Gy | J/kg | m2·s-2 |
dose equivalent | sievert | Sv | J/kg | m2·s-2 |
catalytic activity | katal | kat | - | s-1mol |
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SI Unit Prefixes
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SI Base Units
The International System of Units (SI) define the following base units
Meter (m)
The length of the path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second.
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The US Customary System of Measures
The following are the English System of measurement
Length
12 inches = 1 foot
3 feet = 1 yard
220 yards = 1 furlong
8 furlongs = 1 mile
5 280 feet = 1 mile
1 760 yards = 1 mile
Area
144 square inches = 1 square foot
9 square feet = 1 square yard
4 840 square yards = 1 acre
640 acres = 1 square mile
1 square mile = 1 section
36 sections = 1 township
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Derivation of Heron's / Hero's Formula for Area of Triangle
For a triangle of given three sides, say a, b, and c, the formula for the area is given by
where s is the semi perimeter equal to P/2 = (a + b + c)/2.
Derivation / Proof of Ptolemy's Theorem for Cyclic Quadrilateral
Ptolemy's theorem for cyclic quadrilateral states that the product of the diagonals is equal to the sum of the products of opposite sides. From the figure below, Ptolemy's theorem can be written as
Derivation of Formula for Area of Cyclic Quadrilateral
For a cyclic quadrilateral with given sides a, b, c, and d, the formula for the area is given by
Where s = (a + b + c + d)/2 known as the semi-perimeter.
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001 Solid steel ball remolded into hollow steel ball
Problem 001
A 523.6 cm3 solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.
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001 A wire of given density and total mass
Problem 001
A certain wire that weighs 8.5 g/cc has a total mass of 155 kg.
- What is the density of the wire in kg/m3?
- Find the volume of the wire in cubic centimeter.
- If the total length of the wire is 1500 m, find the cross-sectional area in square millimeters.
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Derivation of Formula for Total Surface Area of the Sphere by Integration
The total surface area of the sphere is four times the area of great circle. To know more about great circle, see properties of a sphere. Given the radius r of the sphere, the total surface area is
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