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Reference
Lee, Stephen (2008). An Introduction to Mathematics for Engineers - Mechanics,
Hodder Education, London.
0-1
Dynamics
The International System of Units – SI units
The base units (7 in total) we will be mainly dealing with in Dynamics are: mass…………. kilogram… kg
The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. length………….metre………m The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. time……………second……..s The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
We will deal with in other topics: temperature .…Kelvin……….K
The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. amount of substance…mole…mol
The mole is the amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol".
The other two are the ampere [A] and candela [cd]
All other units are derived quantities and are based on these units. Some examples are given below.
0-2
Derived units:
Force:
The unit of force is the ‘newton’ (N) defined from Newton’s second law: force = mass x acceleration, or
F=mxa
then 1 newton (N) is the force that will accelerate 1 kg at 1 m/s2
⎡ kgm ⎤
So 1 [N] = 1 ⎢
⎥ note that the terms in square brackets define the unit N in terms
⎣ s2 ⎦ of the fundamental units mass, length, time.
Energy
or work done by a force:
Energy can be quantified by work done by a force:
Work or energy = force x distance, or
W=Fxs
The derived unit for energy is the ‘joule’ (J):
Power can be quantified by the rate of energy transfer i.e. joules per second: power = energy / time = work done / time
P=W/t=Fxs/t
The derived unit for power is the ‘watt’ (W):
⎡ kgm2 ⎤
⎡⎛ kgm ⎞⎛ m ⎞ ⎤
J
Nm
1[W] = 1[ ] = 1[
] = 1⎢⎜ 2 ⎟ ⎜ ⎟⎥ = 1⎢ 3 ⎥ s s
⎢ s ⎥
⎣⎝ s ⎠ ⎝ s ⎠ ⎦
⎣
⎦
0-3
.
Examples of the derived units
Derived quantity
Name
Symbol In other SI units
In SI base units
plane angle
radian
rad
m/m
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, amount joule of heat
J
Nm
m2 kg s–2
power, radiant flux
watt
W
J/s
m2 kg s–3
electric charge, amount of electricity
coulomb
C
electric potential difference, electromotive force
