NEWTON'S FIRST LAW OF MOTION
if the resultant force acting on a particle is zero, the particle
will remain at rest (if originally at rest)
or
will move with constant speed in a straight line (if originally in motion)

NEWTON'S SECOND LAW OF MOTION
F = m a

NEWTON'S THIRD LAW OF MOTION
action and reaction are opposite and equal

NEWTON'S LAW OF GRAVITATION
F = G m₁ m₂ / r²     where G = 6.673 X 10^-11 N•m²/kg²

THE LAW OF FLAT FRICTION
F = μ_s N     where μ_s is coefficient of static friction
F = μ_k N     where μ_k is coefficient of kinetic friction
dry means non-lubricated
wet sometimes means lubricated
wet sometimes means with water

TORQUE
τ = F l
the unit is N•m

WORK
w_{cst force} = F x
the unit is J
note:
1 J = 1 N•m

POWER
P = dw/dt = F v
the unit is watt (W)
note:
1 W = 1 J/s
1 hp = 550 ft•lb/s ≈ 746 W ≈ 0.746 kW ( ≈ ¾ kW )

KINETIC ENERGY
KE = ½ m v²
the unit is J

POTENTIAL ENERGY
PE = m g y
the unit is J

MOMENTUM
P = m v
the unit is kg•m/s

IMPULSE
J = P₂ - P₁     known as impulse-momentum theorem
the unit is kg•m/s

LINEAR ( STRAIGHT-LINE ) MOTION
x = x_o + v_o t + ½ a t²
v = v_o + a t
v² = v_o² + 2 a ( x - x_o )
( x - x_o ) / t = ( v + v_o ) / 2
one of the application is of FREE FALL and normally we define a = - g = - 9.8 m/s²

PROJECTILE MOTION
A projectile is any body that is given an initial velocity & then follows a path determined entirely by the effects of gravitational acceleration & air resistence. The path followed by a projectile is called trajectory. We can treat the x-coordinate & y-coordinate separately, in which a_x = 0 & a_y = - g.

CIRCULAR MOTION
uniform circular motion is the motion of a particle that moves in a circle with constant speed
centripetal means radially inward toward the center
centrifugal means radially outward from the center
centripetal acceleration,    a_rad = v_t² / r

ROTATIONAL MOTION
ω is the angular velocity    ( the unit is rad/s )
v_t = r ω
a_t = r α
a_rad = r ω²
I = ∑ r_i² m_i             ( analogous to m )
τ = I α                    ( analogous to F = m a )
KE = ½ I ω²           ( analogous to KE = ½ m v² )
w_{cst torque} = τ θ       ( analogous to w_{cst force} = F x )
P = τ ω                   ( analogous to P = F v )
L = I ω                   ( analogous to P = m v )
θ = θ_o + ω_o t + ½ α t²
ω = ω_o + α t
ω² = ω_o² + 2 α ( θ - θ_o )
( θ - θ_o ) / t = ( ω + ω_o ) / 2

PERIODIC MOTION @ OSCILLATION
ω is the angular frequency    ( the unit is rad/s )
a periodic motion @ oscillation is a motion that repeats itself in a regular cycle
a simple harmonic motion @ SHM is a motion under the restoring force ( F = - k x ) that is directly proportional to the displacement from equilibrium and ω = 2 π f = ( k / m )^½
the position, velocity & acceleration of SHM are a sinusiodal functions of time
x = A cos ( ω t + Ø )
v = - A ω sin ( ω t + Ø )
a = - A ω² cos ( ω t + Ø )
in a angular SHM,
τ = - k θ              analogous to F = - k x
ω = ( k / I )^½       analogous to ω = ( k / m )^½

GUITAR
below is the fret of guitar :

the ratio of distances of 2 consecutive frets to the bridge is 2^1/12 ( ≈ 1.059463 )
theoretically, the 12^th fret should divide the string in 2 exact halves.
E = 329.6 Hz
B = 246.9 Hz
G, = 196 Hz
D, = 146.8 Hz
A, = 110 Hz
E,, = 82.4 Hz
note:
A' = 440 Hz    ( known as concert pitch )
E = 329.6 Hz
E, = 329.6 / 2 = 164.8 Hz
E,,= 329.6 / 4 = 82.4 Hz

MECHANICAL WAVE
mechanical waves travel thru medium ( solid @ fluid )
electromagnetic waves can travel thru empty space
wave speed,    v = λ f
angular frequency,    ω = v k    where k is the wave number @ propagation constant,    k = 2 π / λ
y ( x , t ) = A sin ω ( t - x / v )
y ( x , t ) = A sin 2 π f ( t - x / v )
y ( x , t ) = A sin 2 π ( t / T - x / λ )
y ( x , t ) = A sin ( ω t - k x )
v = ( F / μ )^½          ( transverse wave )
v = ( B / ρ )^½          ( longitudinal wave - fluid )
v = ( Y / ρ )^½          ( longitudinal wave - solid )
v = ( γ p / ρ )^½         ( longitudinal wave - ideal gas )
v = ( γ R T / M )^½    ( longitudinal wave - ideal gas )

SUPERPOSITION & NORMAL MODES
principle of superposition states that when 2 waves overlap, the actual displacement of any point of on the string, at any time, is obtained by adding the 2 displacements
standing wave is resultant wave based on principle of superposition
reinforcement @ constructive interference occurs when 2 @ more in phase waves passing thru the same region at the same time
cancellation @ destructive interference occurs when 2 @ more out of phase waves passing thru the same region at the same time
resonance occurs if force frequency = normal mode frequency @ force frequency = natural frequency
normal mode of a string ,    f_n = ( n v ) / 2 L = n f₁     ( n = 1, 2, 3........... )
f₁ = 1st normal mode = fundamental frequency
f₂ = 2nd normal mode = 2nd harmonic = 1st overtone
f₃ = 3rd normal mode = 3rd harmonic = 2nd overtone
f₄ = 4th normal mode = 4th harmonic = 3rd overtone
normal mode of air column (open pipe) ,    f_n = ( n v ) / ( 2 L )     ( n = 1, 2, 3........... )
normal mode of air column (stopped pipe) ,    f_n = ( n v ) / ( 4 L )     ( n = 1, 3, 5........... )
terms:
     node (never move at all)
     antinode (amplitude is greatest)
     pressure node = displacement antinode (pressure does not vary)
     pressure antinode = displacement node (pressure variation is greatest)

ACOUSTICS
acoustics is a branch of physics which deals with sound
sound is longitudinal waves in air
noise is unwanted sound
sound can be classified as
     * ultrasonic (with frequency above the range of human hearing)
     * audible (with frequency within the range of human hearing , 20 Hz to 20 kHz)
     * infrasonic (with frequency below the range of human hearing)
intensity,     I   =   ½ ω B k A²   =   p_max² / ( 2 ρ v )   =   p_max² / [ 2 ( ρ B )^½ ]
intensity level @ loudness,     β = ( 10 dB ) log ( I / I_o )     where I_o = 10^-12 W/m²
threshold of pain :     120 dB & 1 W/m² @ 1000 Hz   
threshold of hearing @ audibility :     0 dB & 10^-12 W/m² @ 1000 Hz
noise induced hearing loss :
1) temporary threshold shift
    10 minutes exposed to 120 dB will shift your threshold of hearing from 0 dB to 28 dB
2) permanent threshold shift
    10 years exposed to 92 dB will shift your threshold of hearing from 0 dB to 28 dB
3) acousic trauma
    due to explosion ... etc
beats are heard when 2 tones with slightly different frequencies f₁ and f₂ are sounded together
beat frequency,    f_beat = f₁ - f₂
the pitch of a musical tone is the quality that lets us classify as high or low
it depends primarily on its frequency
eg. using piano
C = 262 Hz
C' = 262 X 2 = 524 Hz ( C' has higher pitch than C )
C" = 262 X 4 = 1048 Hz ( C" has higher pitch than C' )

TEMPERATURE
100^oC = 212^oF = 373 K
0^oC = 32^oF = 273 K
-273^oC = -460^oF = 0 K
note: 10 K is read as ten Kelvin ; not ten degrees Kelvin
T_K = T_C + 273.15
T_F = ( 9 / 5 ) T_C + 32
T_C = ( 5 / 9 )( T_F - 32 )

THERMAL EXPANSION
thermal linear expansion, ΔL = α L_o ΔT
thermal volume expansion, ΔV = β V_o ΔT
example of coefficient of linear expansion :
     aluminium = 2.4 X 10^-5 K^-1 @ (C^o)^-1
     brass = 2.0 X 10^-5 K^-1 @ (C^o)^-1
     copper = 1.7 X 10^-5 K^-1 @ (C^o)^-1
     steel = 1.2 X 10^-5 K^-1 @ (C^o)^-1
example of coefficient of volume expansion :
     aluminium = 7.2 X 10^-5 K^-1 @ (C^o)^-1
     brass = 6.0 X 10^-5 K^-1 @ (C^o)^-1
     copper = 5.1 X 10^-5 K^-1 @ (C^o)^-1
     steel = 3.6 X 10^-5 K^-1 @ (C^o)^-1

LUBRICATION THEORY & FLUID FILM BEARING
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POWER TRANSMISSION
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ROTOR BALANCING
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CONDITION MONITORING OF DYNAMIC EQUIPMENT
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