Basic Units (distance, area, volume, mass, density) ............................2
Mathematical Formulae .......................................................................5
Applied Mechanics .............................................................................10
Thermodynamics.................................................................................21
Fluid Mechanics..................................................................................28
Electricity............................................................................................30
Periodic Table .....................................................................................34
Names in the Metric System
VALUE EXPONENT SYMBOL PREFIX
100 102 h hecto 10 101 da deca 0.1 10-1 d deci 0.01 10-2 c centi 0.001 10-3 m milli 0.000 001 10-6 µ micro
0.000 000 001 10-9 n nano 0.000 000 000 001 10-12 p picoConversion Chart for Metric Units
To
To To To Metre, To To To Milli- Centi- Deci- Gram, Deca- HectoKilo- Litre
1 metre (1 m) = 10 decimetres (10 dm) 12 in. = 1 ft
= 100 centimetres (100 cm) 3 ft = 1 yd
= 1000 millimetres (1000 mm) 5280 ft = 1 mile
1760 yd = 1 mile 1 decametre (1 dam) = 10 m
1 hectometre (1 hm) = 100 m
Conversions:
1 in. = 25.4 mm 1 ft = 30.48 cm
1 mile = 1.61 km 1 yd = 0.914 m 1 m = 3.28 ft
Area
1 sq metre (1 m2) = 10 000 cm2 1 ft2 = 144 in.2 = 1 000 000 mm2 1 yd2 = 9 ft2 1 sq mile = 640 acre = 1 section 1 sq hectometre (1 hm2) = 10 000 m2
= 1 hectare (1 ha)
1 sq km (1 km2) = 1 000 000 m2
Conversions:
2 = 6.45 cm2 = 645 mm2 2 = 10.8 ft21 m 1 acre = 0.405 ha
1 sq mile = 2.59 km2
1 m3 = 1 000 000 cm3 1 ft3 = 1728 in.3 = 1 x 109 mm3 1 yd3 = 27 ft3
1 dm3 = 1 litre 1(liquid) U.S. gallon = 231 in.3
1 litre = 1000 cm
3 = 4 (liquid) quarts
1 mL = 1 cm3 1 U.S. barrel (bbl) = 42 U.S. gal.
1 m3 = 1000 litres 1 imperial gallon = 1.2 U.S. gal.
Conversions:
3 31 in. 3 31 m 1 litre = 61 in.3
1 U.S.gal = 3.78 litres
1 U.S. bbl = 159 litres
1 litre/s = 15.9 U.S. gal/min
Mass and Weight
1 kilogram (1 kg) = 1000 grams 1000 kg = 1 tonne 2000 lb = 1 ton (short) 1 long ton = 2240 lb
Conversions:
1 kg (on Earth) results in a weight of 2.2 lb
Density
mass
density
=
mass weight density =weight volume volume
ρ
=
m › kg žρ = w › lb ž V œm3Ÿ V œft3 Ÿ
(on Earth) a mass density of 1 kg3 results in a weight density of 0.0623 lb3m ftSI Imperial
In SI R.D. is a comparison of mass density to a standard. For solids and liquids the standard is fresh water.
water.
In Imperial the corresponding quantity is specific gravity; for solids and liquids a comparison of weight density to that of
In both systems the same numbers hold for R.D. as for S.G. since these are equivalent ratios.
RELATIVE DENSITY (SPECIFIC GRAVITY) OF VARIOUS SUBSTANCESWater (fresh)...............1.00 Mica............................2.9
Water (sea average) ....1.03 Nickel .........................8.6
Aluminum...................2.56 Oil (linseed) ................0.94 Antimony....................6.70 Oil (olive) ...................0.92 Bismuth.......................9.80 Oil (petroleum) ...........0.76-0.86 Brass ...........................8.40 Oil (turpentine) ...........0.87 Brick ...........................2.1 Paraffin .......................0.86 Calcium.......................1.58 Platinum....................21.5 Carbon (diamond).......3.4 Carbon (graphite)........2.3 Carbon (charcoal) .......1.8 Sand (dry) ...................1.42 Silicon.........................2.6 Silver.........................10.57
Chromium...................6.5 Slate ............................2.1-2.8 Clay.............................1.9 Sodium........................0.97 Coal.............................1.36-1.4 Steel (mild) .................7.87 Cobalt .........................8.6 Sulphur .......................2.07 Copper ........................8.77 Tin...............................7.3 Cork ............................0.24 Tungsten ...................19.1 Glass (crown)..............2.5 Wood (ash) .................0.75
Glass (flint).................3.5 Wood (beech) .............0.7-0.8 Gold ..........................19.3 Wood (ebony).............1.1-1.2 Iron (cast)....................7.21 Wood (elm).................0.66
Iron (wrought) ............7.78 Wood (lignum-vitae) ..1.3
Lead ..........................11.4 Wood (oak).................0.7-1.0 Magnesium .................1.74 Wood (pine)................0.56 Manganese..................8.0 Wood (teak) ................0.8 Mercury ....................13.6 Zinc.............................7.0
Alpha α Beta β Gamma γ Delta Epsilon ε Zeta ζ Eta η Theta θ Pi Omega &, ω Iota ι Rho ρ Kappa κ Sigma Σ, σ Lambda λ Tau τ Mu µ Upsilon υ Nu ν Phi Φ, φ Xi ξ Kai χ Omicron Ο Psi ψ
MATHEMATICAL FORMULAE(x + y)2 = x2 + 2xy + y2
(x - y)2 = x2 - 2xy + y2
x2 - y2 = (x - y) (x + y)
(x + y)3 = x3 + 3x2y + 3xy2 + y3
x3 + y3 = (x + y) (x2 - xy + y2)
(x - y)3 = x3 - 3x2y + 3xy2 - y3
x3 - y3 = (x - y) (x2 + xy + y2)
2. Quadratic Equation
If ax + bx + c = 0,
-b± b2−4acThen x = 2a
Trigonometry
Sin
=
y , cos =x , tan =y h h x
2. Pythagoras' Law
x2 + y2 = h2
3. Trigonometric Function Values
Sin is positive from 0° to 90° and positive from 90° to 180°
Cos is positive from 0° to 90° and negative from 90° to 180°
Tan is positive from 0° to 90° and negative from 90° to 180°
4. Solution of Triangles
a= b= c Sin A Sin B Sin C
b. Cosine Law
c2 = a2 + b2 - 2 ab Cos C
a2 = b2 + c2 - 2 bc Cos A
b2 = a2 + c2 - 2 ac Cos B
Geometry
Area
=
base x perpendicular height 2
=
bcSin A= ab Sin C= acSin B 2 2 2
Area= s(s-a)(s-b) (s-c)
where, s is half the sum of the sides, or s = a + b c 2
b. Equilateral TrianglesArea = 0.433 x side2
2. Circumference of a Circle
C = πd
3. Area of a Circle
A =
π
r
2 = circumference x r= πd2 = 0.7854d2 2 4
4. Area of a Sector of a Circle
A =
arcx r 2
A =
θ
°
r2
(θ = angle in radians)
2
5. Area of a Segment of a Circle
A = area of sector – area of triangle
Also approximate area =4 h2 d -0.6083 h
6. Ellipse
A = π Dd4
Approx. circumference =
7. Area of Trapezoid
A = › +bžhœ Ÿ
8. Area of Hexagon
A = 2.6s2 where s is the length of one side
9. Area of Octagon
A = 4.83s2 where s is the length of one side
10. Sphere
Total surface area A =4πr2
Surface area of segment As = πdh
Volume V =
4 πr3 3
Volume of segment
V
s
=
π
h2
3 (3r – h)
Vs =π h 2+3a2) where a = radius of segment base6 (h
11. Volume of a Cylinder
V = πd2L where L is cylinder length 4
12. Pyramid
Volume
V = 1 base area x perpendicular height
3
Volume of frustum
VF = h (A +a + Aa) where h is the perpendicular height, A and a are areas as shown 3
13. Cone
Area of curved surface of cone:
A =
πDL 2
A
F
=
π +d)L 2
V= base area
× perpendicular height 3
Volume of frustum:
= perpendicular height×π (R2 + r2+Rr)VF 3
APPLIED MECHANICS
Vector - a property described by a magnitude and a direction
Velocity - vector property equal to displacement
time
The magnitude of velocity may be referred to as speed
In SI the basic unit is ms , in Imperial ft Other common units are kmh , mi
m ftConversions: 1 =3.28
s s
km mi1 =0.621
h h
Speed of sound in dry air is 331 ms at 0°C and increases by about 0.61 ms for each °C rise
Speed of light in vacuum equals 3 x 10 8 m
s
Acceleration - vector property equal to change in velocity
time
In SI the basic unit is
s
2
m , in Imperial
ft s2
Conversion
: 1
s
2
m = 3.28
ft s2
Acceleration due to gravity, symbol "g", is 9.81 m or 32.2 ft s2 s2
u initial velocity v final velocity t elapsed time s displacement a acceleration
v=u+at
2
s = ut + 12 at2
v2=u2+2as
Angular Velocity and Acceleration
θ angular displacement (radians)
ω angular velocity (radians/s); ω1 = initial, ω2 = final α angular acceleration (radians/s2)
θ = ω1 + ω2 x t 2
θ = ω1 t + ½ α t2
ω22 = ω12 + 2 α θ
linear displacement, s = r θ linear velocity, v = r ω linear, or tangential acceleration, aT = r
Tangential, Centripetal and Total AccelerationTangential acceleration aT is due to angular acceleration α
aT = rα
Centripetal (Centrifugal) acceleration ac is due to change in direction only
ac = v2/r = r ω2
Total acceleration, a, of a rotating point experiencing angular acceleration is the vector sum of aT and ac
a = aT + ac
In SI the unit of force is the newton, N, defined as a kg m2s
In Imperial the unit of force is the pound lb
Conversion: 9.81 N = 2.2 lb
Weight
The gravitational force of attraction between a mass, m, and the mass of the Earth
In SI weight can be calculated from
Weight = F = mg , where g = 9.81 m/s2
In Imperial, the mass of an object (rarely used), in slugs, can be calculated from the known weight in pounds
m= Weightg g=32.2ft2s
Newton's Second Law of Motion
An unbalanced force F will cause an object of mass m to accelerate a, according to:
F = ma (Imperial F = wg a, where w is weight)
Torque Equation
T = I α where T is the acceleration torque in Nm, I is the moment of inertia in kg m2 and α is the angular acceleration in radians/s2
Momentum
Vector quantity, symbol p,
p = mv (Imperial p = wg v, where w is weight)
in SI unit is kg ms
Work
Scalar quantity, equal to the (vector) product of a force and the displacement of an object. In simple systems, where W is work, F force and s distance
W = F s
In SI the unit of work is the joule, J, or kilojoule, kJ