Basic SI units are shown in Table 1
|
Quantity
|
Unit
|
Symbol
|
Definition
|
|
Length
|
meter
|
m
|
1983, 17th CGPM: The path travelled by light
in vacuum during a time interval of 1/299792458 seconds. This fixes the speed
of light to exactly 299792458 m/s.
|
|
Mass
|
kilogram
|
kg
|
1901, 3rd CGPM: Mass of the platinum-iridium
prototype at BIPM in Sevres.
|
|
Time
|
second
|
s
|
1968, 13th CGPM: One second equals 9192631770
periods of the radiation due to the transition between the two hyperfine
levels of the ground state of Cesium 133.
|
|
Electric current
|
ampere
|
A
|
1948, 9th CGPM: Given two parallel,
rectilinear conductors of negligible circular cross-section positioned 1 m
apart in vacuum, one ampere is the electric current which, passing through
both of them, makes them attract each other by the force of 2.10-7 newtons
per every meter of length. This fixes the permeability of vacuum to exactly 2π*10-7 H/m.
|
|
Temperature
|
kelvin
|
K
|
1968, 13th CGPM: One degree K equals 1/273.16
of the thermodynamic temperature of the triple point of water.
|
|
Quantity of substance
|
mole
|
mol
|
1971, 14th CGPM: The amount of a
substance composed of as many specified elementary units (molecules,
atoms) as there are atoms in 0.012 kg of Carbon 12.
|
|
Luminosity
|
candle
|
cd
|
1979, 16th CGPM: The candle (or candela) is
the luminous intensity, in a given direction, of a source that emits
monochromatic radiation of frequency 540.1012 hertz
and that has a radiant intensity in that direction of 1/683 W/sr.
|
Derived
SI units
|
Quantity
|
Unit
|
Symbol
|
Equals
|
Definition / Note
|
|
Space and time:
|
||||
|
Plane
angle
|
radian
|
rad
|
|
The plane
angle which, when centered in a circle,
cuts off an arc whose length is equal to the circle radius.
|
|
Solid
angle
|
steradian
|
sr
|
|
The solid
angle which, when centered in a sphere,
cuts off a cap whose surface equals that of a square having the radius as
side.
|
|
Frequency
|
hertz
|
Hz
|
1 s-1
|
[number of
events or cycles]/[time].
|
|
Mechanics:
|
||||
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Force
|
newton
|
N
|
1 kg.m.s-2
|
[mass].[acceleration].
|
|
Pressure
|
pascal
|
Pa
|
1 N.m-2
|
[force]/[area].
Also: stress.
|
|
Energy
|
joule
|
J
|
1 N.m
|
[force].[length].
Also: Work, Heat
|
|
Power
|
watt
|
W
|
1 J.s-1
|
[energy]/[time].
Also: Radiant flux
|
|
Thermodynamics:
|
||||
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Temperature
|
celsius
|
oC
|
1 K
|
T [oC] = T [K] -273.15 (the offset is
exact!).
|
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Electromagnetism:
|
||||
|
Charge
|
coulomb
|
C
|
1 A.s
|
[current].[time].
|
|
Potential
|
volt
|
V
|
1 W.A-1
|
[power]/[current].
Only differences are measurable!
|
|
Resistance
|
ohm
|
Ω
|
1 V.A-1
|
[Δpotential]/[current].
|
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Conductance
|
siemens
|
S
|
1 A.V-1
|
[current]/[Δpotential].
|
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Capacitance
|
farad
|
F
|
1 C.V-1
|
[charge]/[Δpotential].
|
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Inductance
|
henry
|
H
|
1 V.s.A-1
|
[Δpotential]/[rate
of change of current].
|
|
Magnetic
flux
|
weber
|
Wb
|
1 J.A-1
|
[energy]/[current].
|
|
Magnetic
flux density
|
tesla
|
T
|
1 Wb.m-2
|
[magnetic
flux]/[area]. Also magnetic induction.
|
|
Optics:
|
||||
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Luminous
flux
|
lumen
|
lm
|
1 cd.sr
|
[luminosity].[solid
angle].
|
|
Illuminance
|
lux
|
lx
|
1 lm.m-2
|
[luminous
flux]/[area].
|
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Convergence
|
dioptry
|
dioptry
|
1 m-1
|
Inverse of
focal length.
|
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Radioactivity and radiation:
|
||||
|
Activity
|
becquerel
|
Bq
|
1 s-1
|
[number of
decay events]/[time].
|
|
Absorbed
dose
|
gray
|
Gy
|
1 J.kg-1
|
[energy]/[mass].
|
|
Dose
equivalent
|
sievert
|
Sv
|
1 J.kg-1
|
[energy]/[mass].
Absorbed dose re-normalized by biological effects.
|
|
Chemistry:
|
||||
|
Katalytic
activity
|
katal
|
kat
|
1 mol.s-1
|
[quantity
of substance]/[time].
|
$$\begin{align} & x=4\text{ m} \\ & \underline{y=3\text{ m}} \\ & r=\sqrt{{{x}^{2}}+{{y}^{2}}}=\sqrt{{{4}^{2}}+{{3}^{2}}}=\sqrt{16+9}=\sqrt{25}=5\text{ m} \\ \end{align}$$
3. Body
is traveling along the x axis. The movement of the body is defined as: Δx=x2-x1
where x1 is starting position and x2 is ending position Determine:
a)Distance that body traveled if the coordinates
of body positions are: x1 = 4 m and x2 = 10m?
$$\begin{align}
& {{x}_{1}}=4\text{ m} \\
& \underline{{{x}_{2}}=10\text{ m}} \\
& \Delta x={{x}_{2}}-{{x}_{1}}=10-4=6\text{ m} \\
\end{align}$$
b) Distance that body traveled if the coordinates
of body starting and ending positions are: x1 = 5 m and x2 = 12m?
$$\begin{align}
& {{x}_{1}}=5\text{ m} \\
& \underline{{{x}_{2}}=12\text{ m}} \\
& \Delta x={{x}_{2}}-{{x}_{1}}=12-5=7\text{ m} \\
\end{align}$$
c) Distance that body traveled if the coordinates of
body starting and ending positions are: x1 = -5 m and x2 = 9m?
$$\begin{align}
& {{x}_{1}}=-5\text{ m} \\
& \underline{{{x}_{2}}=9\text{ m}} \\
& \Delta x={{x}_{2}}-{{x}_{1}}=9+5=14\text{ m} \\
\end{align}$$
d) Distance that body traveled if the coordinates of
body starting and ending positions are: x1 = -10 m and x2 = 9m?
$$\begin{align}
& {{x}_{1}}=-10\text{ m} \\
& \underline{{{x}_{2}}=9\text{ m}} \\
& \Delta x={{x}_{2}}-{{x}_{1}}=9+10=19\text{ m} \\
\end{align}$$
a) When car is moving from position A to position B
determine the shift?
$$x=\sqrt{{{r}^{2}}+{{r}^{2}}}=r\sqrt{2}$$
b) Car is moving from position A to position B so
determine the traveled path?
$$\begin{align}
& \underline{r,\varphi =\frac{3}{2}\pi } \\
& s=? \\
& s=\frac{3}{2}\pi r \\
\end{align}$$
5. The pressure is pressing down the material with pressure equal to 10MPa. Express the value in scientific notation.
$$p=10\text{ MPa}=10\cdot {{10}^{6}}\text{ Pa}$$
6. The distance traveled is 5·105 mm. How much is that in m, dm and cm?
$$\begin{align}
& \underline{s=5\cdot {{10}^{5}}\text{ mm}} \\
& s=5\cdot {{10}^{5}}\text{ }\left[ \text{mm} \right]\frac{\text{1 }\left[ \text{m} \right]}{1000\text{ }\left[ \text{mm} \right]}=5\cdot {{10}^{2}}\text{ m} \\
& s=5\cdot {{10}^{5}}\text{ }\left[ \text{mm} \right]\frac{\text{1 }\left[ \text{dm} \right]}{100\text{ }\left[ \text{mm} \right]}=5\cdot {{10}^{3}}\text{ dm} \\
& s=5\cdot {{10}^{5}}\text{ }\left[ \text{mm} \right]\frac{\text{1 }\left[ \text{cm} \right]}{10\text{ }\left[ \text{mm} \right]}=5\cdot {{10}^{4}}\text{ cm} \\
\end{align}$$
6. The distance traveled is 5·105 mm. How much is that in m, dm and cm?
7. Volume of some object is 500 cm3. How much
is that in m3, dm3 and cm3?
$$\begin{align} & \underline{s=500\text{ c}{{\text{m}}^{3}}} \\ & 1\text{ }{{\text{m}}^{\text{3}}}=100000\text{ c}{{\text{m}}^{3}} \\ & s=500\text{ }\left[ \text{c}{{\text{m}}^{3}} \right]\frac{\text{1 }\left[ {{\text{m}}^{3}} \right]}{{{10}^{5}}\text{ }\left[ \text{c}{{\text{m}}^{3}} \right]}=500\cdot {{10}^{-5}}\text{ }{{\text{m}}^{3}}=5\cdot {{10}^{-3}}\text{ }{{\text{m}}^{3}} \\ & 1\text{ d}{{\text{m}}^{\text{3}}}=1000\text{ c}{{\text{m}}^{3}} \\ & s=500\text{ }\left[ \text{c}{{\text{m}}^{3}} \right]\frac{\text{1 }\left[ \text{d}{{\text{m}}^{3}} \right]}{1000\text{ }\left[ \text{c}{{\text{m}}^{3}} \right]}=0.5\text{ d}{{\text{m}}^{3}} \\ & 1\text{ c}{{\text{m}}^{3}}=1000\text{ m}{{\text{m}}^{3}} \\ & s=500\text{ }\left[ \text{c}{{\text{m}}^{3}} \right]\frac{\text{1000 }\left[ \text{m}{{\text{m}}^{3}} \right]}{1\text{ }\left[ \text{c}{{\text{m}}^{3}} \right]}=5\cdot {{10}^{5}}\text{ m}{{\text{m}}^{3}} \\
\end{align}$$
8. The speed of light is approximately 3·108
m/s. How much is that in km/h and cm/min?
-
$$\begin{align}
& \underline{v=3\cdot {{10}^{8}}\text{ m/s}} \\
& v=3\cdot {{10}^{8}}\text{ }\left[ \frac{\text{m}}{s} \right]\frac{1\text{ }\left[ \text{km} \right]}{1000\text{ }\left[ \text{m} \right]}\frac{3600\text{ }\left[ \text{s} \right]}{1\text{ }\left[ \text{h} \right]}=1.08\cdot {{10}^{9}}\text{ km/h} \\
& v=3\cdot {{10}^{8}}\text{ }\left[ \frac{\text{m}}{s} \right]\frac{100\text{ }\left[ \text{cm} \right]}{1\text{ }\left[ \text{m} \right]}\frac{\text{60 }\left[ s \right]}{1\left[ \min \right]}=1.8\cdot {{10}^{12}}\text{cm/min} \\
\end{align}$$
- 9. One liter of volume is equal to 1 dm3.How
much is that in m3?
10. Length of cuboid sides are 5 cm x 3 cm x 6 cm.
a) Determine
the volume of cuboid and express it in m3 cm3 and mm3.
b) Calculate
the area of each cuboids side and express it in m3 cm3
and mm3
c)What is cuboids volume in liters?
d) Determine
the density of cuboid’s material if a mass of cuboid is equal to 1 kg.
$$\begin{align}
& a=5\text{ cm }=\text{ 0}\text{.05 m} \\
& b=3\text{ cm }=\text{ 0}\text{.03 m} \\
& \underline{c=6\text{ cm }=\text{ 0}\text{.06 m}} \\
& a)V=?\text{ }{{\text{m}}^{3}},\text{ c}{{\text{m}}^{\text{3}}}\text{ }\text{, m}{{\text{m}}^{3}} \\
& V=abc=0.05\cdot 0.03\cdot 0.06=9\cdot {{10}^{-5}}{{\text{m}}^{3}} \\
& 1\text{ }{{\text{m}}^{3}}=1\cdot {{10}^{6}}\text{c}{{\text{m}}^{\text{3}}} \\
& V=9\cdot {{10}^{-5}}\cdot 1\cdot {{10}^{6}}=90\text{ c}{{\text{m}}^{\text{3}}} \\
& 1\text{ }{{\text{m}}^{3}}=1\cdot {{10}^{9}}\text{ m}{{\text{m}}^{3}} \\
& V=9\cdot {{10}^{-5}}\cdot 1\cdot {{10}^{9}}=90000\text{ m}{{\text{m}}^{\text{3}}} \\
& b)\text{ Number of cuboid sides is }n=\text{ }6 \\
& \text{Two sides of cuboid are the same and that means that there are three differnet sides} \\
& I)\text{ }a=5\text{ cm }=\text{ 0}\text{.05 m} \\
& b=3\text{ cm }=\text{ 0}\text{.03 m} \\
& {{P}_{1}}=ab=5\cdot 3=15\text{ c}{{\text{m}}^{2}}=15\text{ }\left[ \text{c}{{\text{m}}^{2}} \right]\frac{1\text{ }\left[ {{\text{m}}^{2}} \right]}{1000\text{ }\left[ \text{c}{{\text{m}}^{2}} \right]}=0.015\text{ }{{\text{m}}^{2}}=0.015\text{ }\left[ {{\text{m}}^{2}} \right]\frac{1\cdot {{10}^{6}}\left[ \text{m}{{\text{m}}^{2}} \right]}{1\text{ }\left[ {{\text{m}}^{\text{2}}} \right]}=15000\text{ m}{{\text{m}}^{2}} \\
& {{P}_{2}}=ac=5\cdot 6=30\text{ c}{{\text{m}}^{2}}=30\text{ }\left[ \text{c}{{\text{m}}^{2}} \right]\frac{1\text{ }\left[ {{\text{m}}^{2}} \right]}{1000\text{ }\left[ \text{c}{{\text{m}}^{2}} \right]}=0.03\text{ }{{\text{m}}^{2}}=0.03\text{ }\left[ {{\text{m}}^{2}} \right]\frac{1\cdot {{10}^{6}}\left[ \text{m}{{\text{m}}^{2}} \right]}{1\text{ }\left[ {{\text{m}}^{\text{2}}} \right]}=30000\text{ m}{{\text{m}}^{2}} \\
& {{P}_{3}}=bc=3\cdot 6=18\text{ c}{{\text{m}}^{2}}=18\text{ }\left[ \text{c}{{\text{m}}^{2}} \right]\frac{1\text{ }\left[ {{\text{m}}^{2}} \right]}{1000\text{ }\left[ \text{c}{{\text{m}}^{2}} \right]}=0.018\text{ }{{\text{m}}^{2}}=0.018\text{ }\left[ {{\text{m}}^{2}} \right]\frac{1\cdot {{10}^{6}}\left[ \text{m}{{\text{m}}^{2}} \right]}{1\text{ }\left[ {{\text{m}}^{\text{2}}} \right]}=18000\text{ m}{{\text{m}}^{2}} \\
& c)V=?\text{ L} \\
& V=90\text{ c}{{\text{m}}^{\text{3}}}=90\text{ }\left[ c{{m}^{3}} \right]\cdot \frac{1\text{ }\left[ \text{d}{{\text{m}}^{3}} \right]}{1000\left[ c{{m}^{3}} \right]}=0.09\text{ d}{{\text{m}}^{3}}=0.09L \\
& d)m=1kg \\
& V=9\cdot {{10}^{-5}}{{\text{m}}^{3}} \\
& \rho =\frac{m}{V}=\frac{1}{9\cdot {{10}^{-5}}}=11111.1\text{ kg/}{{\text{m}}^{3}} \\
\end{align}$$
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