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Chapter 2: Motion along A Straight Line
s = speed 
t = time 
Total Distance 
xf +xi 
One Dimensional Motion 
Distance 
d = s⋅t 
Displacement 
xf xi 
Speed 
(xf +xi ) / (tf +t i`) 
Not Constant Velocity 
Average Velocity 
(xf xi ) / (tf t i`) 
x↑: v+ x↓: v x→: v=0 
a+: v↑ a: v↓ a=0: v→ 
Instantaneous Acceleration 
(vf vi ) / (tf t i`) 
Constant Acceleration in 1D 
Vf = Vi + (a⋅t) 
Constant Acceleration Final Distance 
Xf = 1/2(Vf Vi ) ⋅ t 
Xf = Xi + (Vi ⋅ t) + 1/2(a ⋅ t) 
a = (Vf Vi ) / t 
t = (Vf Vi ) / a 
Vf = Vi ⋅ a^{2} 
Vf ^{2} = Vi ^{2} + 2⋅a (xf xi ) 
Gy = 9.8 m/s 
Chapter 14: Periodic Motion
Angular Frequency 
w = 2πf 2π/T 
Frequency 
f = 1 / T 
Period 
T = 1 / f 
Restoring Force 
Fx = kx 
Simple Harmonic Motion 
k = Spring Constant 
x = displacement 
m = mass 
Displacement as function of time 
x = Acos(wt + Θ) 
Velocity as function of time 
v = wAsin(wt + Θ) 
Acceleration as function of time 
a = w^{2}Acos(wt + Θ) 
xmax = A [Amplitude] 
xmax = A [Amplitude] 
vmax = wA 
vmax = wA 
amax = w^{2}A 
amax = w^{2}A 
Equation for Simple Harmonic Motion 
a`x =  (k/m) x 
k = restoring force 
Angular Frequency for SHM 
w = √k/m 
Frequency for SHM 
f = w/2π 

f = 1/2π√k/m 
Period for SHM 
T = 1/f 

T = 2π/w 

T = 2π√m/k 
Total Mechanical Energy (Constant) 
E = 1/2mvx ^{2} + 1/2kx^{2} 

E = 1/2kA^{2} 


Chapter 6: Work and Kinetic Energy
1km = 1000m 
1 kg = 1000g 
Dot Product 
P = Power 
A⋅B = (Ai ⋅Bi )+(Aj ⋅Bj ) 
t = s 
Work = Force ⋅ distance 
W = Fx ⋅ distance 
W = F⋅cosΘ⋅distance 
KE : 1/2⋅m⋅v^{2} 
U = m⋅g⋅h 
Wtotal = KE f  KE i 
Wx = F (cosΘ)⋅s  Wy = F (sinΘ)⋅s 
Constant Speed 
Friction (opposite) = cos(180^{o}) 
P = F⋅v 
P = (W/t) 
Pav = ΔW / Δt [Average Power] 
if F→ & s← =  W 
if F↓ & s→ = 0 
if F→ & s→ = W 
Force Required to Stretch a spring 
Fx = k ⋅ x 
Chapter 13: Newton's Law of Gravitation
GE = 6.67⋅10^{11} 
Earth Gravity Constant 
RE = 6.38⋅10^{6} m 
Earth Radius 
ME = 5.972⋅10^{24} kg 
Mass of Earth 
g = 9.8 m/s; ag = 9.8 m/s 
r  RE = h 
Fg = (GE ⋅m1 ⋅m2 ) / (r^{2}) 
Fg = m ⋅ a 
w = m⋅g 
s = r  RE cosΘ 
Gravitation and Spherically Symmetric Bodies 
Fg = (GE ⋅mE ⋅m) / (r^{2}) 
Weight of the body at Earth's Surface 
w = Fg = (GE ⋅mE ⋅m) / (RE ^{2}) 
Acceleration due to Gravity 
g = (GE ⋅mE ) / (RE ^{2}) 
Velocity of Earth 
VE = 4/3πRE ^{2} = 1.08⋅10^{21} m^{3} 
Gravitational Potential Energy 
U = (GE ⋅mE ⋅m) / (r) 
WorkDone by Gravity 
Wgrav = m⋅g(r1 r2 ) 
Wgrav = GmE ⋅m ⋅ (r1 r2 ) / (r1 ⋅r2 ) 
Wgrav = GmE ⋅m ⋅ (r1 r2 ) / (RE ^{2}) 
[if the body stays close to Earth] 
Speed of the Satellite 
v = √(G⋅mE / r) 
Period of Circular Orbit 
T = (2πr / v) 
T = 2πr^{3/2}/√G⋅mE 
T = 2πr √(r / G⋅mE ) 
Point Mass Outside a Spherical Shell 
Ui =  Gm⋅mi / s 
Apparent weight ; Earth's Rotation 
w0 = true weight of object 
F = force exerted by spring scale 
F + w0 = net force on object 
w = apparent weight = opposite of F 
centripetal acceleration` 
w0  F = (mv^{2} / RE ) 

w = w0  (mv^{2} / RE ) 
freefall acceleration 
g = g0  (v^{2}/ RE ) 
Black Holes 
P = Density 
P = M / v 
v = 4/3πR^{3} 
c = speed of light in the vaccum 
Schwardzschild Radius 
Rs = 2GM / c^{2} 
c = √2GM / RS 


Chapter 7: Potential Energy, Energy Conservation
Yaxis E = Mechanical Energy 
Wgrav = F ⋅ s = w(y1 y2 ) 
Wgrav =(m⋅g⋅y1 )(m⋅g⋅y1 ) 
Wgrav =Ugrav,1  Ugrav,2 
Wgrav = Δ Ugrav 
Conservation of Mechanical Energy 
Kf Ki = Ugrav,1  Ugrav,2 
Ki +Ugrav,1 =Kf +Ugrav,2 
E = K + Ugrav = constant (if gravity does work) 
When other forces than Gravity do work 
Wother + Wgrav = Kf  Ki 
Elastic Potential Energy 
Uel = 1/2kx^{2} 
Work Done a Spring 
W = 1/2kx2 ^{2}  1/2kx1 ^{2} 
If Elastic does work, total mechanical energy is stored 
Ki +Uel,1 =Kf +Uel,2 
Situations with Both Gravitational and Elastic Potential Energy 
K1 +U1 +Wother =K2 +U2 
The work done by all forces other than the gravitational force or elastic force equals the change in total mechanical energy E = K + U of the system 
The Law of Conservation of Energy 
ΔUint = Wother ΔUint = internal energy 
Force and Potential Energy 
Fx (x) =  dU(x) / dx 
Chapter 14: Periodic Motion (cont.)
The Simple Pendelum (TSP) 
L = pendulum length 
Angular Frequency TSP 
w = √k/m 

w = √mg / L /m 

w = √g/L 
Frequency TSP 
f = w/2π 

f = 1/2π √g/L 
Period TSP 
T = 2π/w 

T = 1/f 

T = 2π√L/g 
The Physical Pendulum (TPP) 
L = angular momentum 
L = mvr 
w = Angular Velocity 
w = ΔΘ / Δt 
(I)nertia = L / w 
Angular Frequency TPP 
w = √mgd / I 
Period TPP 
T = 2π √ I / mgd 
Damped Oscillation 
b = Damping Constant 
Displace of Damped 
x = Ae^{b(2m)t} cost (wt + Θ) 
Angular Frequency of Damped 
w' = √ (k/m)  (b^{2} / 4m^{2}) 
Force Oscillations and Resonance 
Fmax = Maximum Driving Force 
k = constant restoring force 
wd = Driving Angular Frequency 
A = Fmax / √(kmwd ^{2})^{2} + b^{2}wd ^{2} 

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