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Chapter 2: Motion along A Straight Line
s = speed 
t = time 
Total Distance 

One Dimensional Motion 
Distance 
d = s⋅t 
Displacement 

Speed 

Not Constant Velocity 
Average Velocity 

x↑: v+ x↓: v x→: v=0 
a+: v↑ a: v↓ a=0: v→ 
Instantaneous Acceleration 

Constant Acceleration in 1D 

Constant Acceleration Final Distance 

X f
= X i
+ (V i
⋅ t) + 1/2(a ⋅ t) 



V f ^{2} = V i ^{2} + 2⋅a (x f
x i
) 

Chapter 14: Periodic Motion
Angular Frequency 
w = 2πf 2π/T 
Frequency 
f = 1 / T 
Period 
T = 1 / f 
Restoring Force 

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) 






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 = 1/2mv x ^{2} + 1/2kx ^{2} 

E = 1/2kA^{2} 


Chapter 6: Work and Kinetic Energy
1km = 1000m 
1 kg = 1000g 
Dot Product 
P = Power 

t = s 
Work = Force ⋅ distance 

W = F⋅cosΘ⋅distance 

U = m⋅g⋅h 

W x
= F (cosΘ)⋅s  W y
= F (sinΘ)⋅s 
Constant Speed 
Friction (opposite) = cos(180^{o}) 
P = F⋅v 
P = (W/t) 
P av
= ΔW / Δt [Average Power] 
if F→ & s← =  W 
if F↓ & s→ = 0 
if F→ & s→ = W 
Force Required to Stretch a spring 

Chapter 13: Newton's Law of Gravitation

Earth Gravity Constant 

Earth Radius 

Mass of Earth 
g = 9.8 m/s; a g
= 9.8 m/s 

F g
= (G E
⋅m 1
⋅m 2
) / (r ^{2}) 

w = m⋅g 

Gravitation and Spherically Symmetric Bodies 

Weight of the body at Earth's Surface 
w = F g
= (G E
⋅m E
⋅m) / (R E ^{2}) 
Acceleration due to Gravity 

Velocity of Earth 
V E
= 4/3πR E ^{2} = 1.08⋅10 ^{21} m ^{3} 
Gravitational Potential Energy 

WorkDone by Gravity 

W grav
= Gm E
⋅m ⋅ (r 1
r 2
) / (r 1
⋅r 2
) 
W grav
= Gm E
⋅m ⋅ (r 1
r 2
) / (R E ^{2}) 
[if the body stays close to Earth] 
Speed of the Satellite 

Period of Circular Orbit 
T = (2πr / v) 


Point Mass Outside a Spherical Shell 

Apparent weight ; Earth's Rotation 
w 0
= true weight of object 
F = force exerted by spring scale 
F + w 0
= net force on object 
w = apparent weight = opposite of F 
centripetal acceleration` 



freefall acceleration 

Black Holes 
P = Density 
P = M / v 
v = 4/3πR^{3} 
c = speed of light in the vaccum 
Schwardzschild Radius 




Chapter 7: Potential Energy, Energy Conservation
Yaxis E = Mechanical Energy 




Conservation of Mechanical Energy 
K f
K i
= U grav,1
 U grav,2


E = K + U grav
= constant (if gravity does work) 
When other forces than Gravity do work 

Elastic Potential Energy 

Work Done a Spring 
W = 1/2kx 2 ^{2}  1/2kx 1 ^{2} 
If Elastic does work, total mechanical energy is stored 

Situations with Both Gravitational and Elastic Potential Energy 

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 
ΔU int
= W other ΔU int
= internal energy 
Force and Potential Energy 

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 
F max
= Maximum Driving Force 
k = constant restoring force 
w d
= Driving Angular Frequency 
A = F max
/ √(kmw d ^{2}) ^{2} + b ^{2}w d ^{2} 

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