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Physics Final Cheat Sheet Cheat Sheet by

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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+ti`)
Not Constant Velocity
Average Velocity
(xf-xi) / (tf-ti`)
x↑: v+
x↓: v-
x→: v=0
a+: v↑
a-: v↓
a=0: v→
Instan­taneous Accele­ration
(vf-vi) / (tf-ti`)
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⋅ a2
Vf2 = Vi2 + 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 = -w2Acos(wt + Θ)
xmax = A [Ampli­tude]
-xmax = A [Ampli­tude]
vmax = wA
-vmax = wA
amax = w2A
-amax = w2A
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 = 1/2mvx2 + 1/2kx2
 
E = 1/2kA2
 

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⋅v2
U = m⋅g⋅h
Wtotal = KEf - KEi
Wx = F (cosΘ)⋅s || Wy = F (sinΘ)⋅s
Constant Speed
Friction (opposite) = cos(180o)
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⋅106 m
Earth Radius
ME= 5.972⋅1024 kg
Mass of Earth
g = 9.8 m/s; ag = 9.8 m/s
r - RE = h
Fg = (GE⋅m1⋅m2) / (r2)
Fg = m ⋅ a
w = m⋅g
s = r - RE cosΘ
Gravit­ation and Spheri­cally
Symmetric Bodies
Fg = (GE⋅mE⋅m) / (r2)
Weight of the body at Earth's Surface
w = Fg = (GE⋅mE⋅m) / (RE2)
Accele­ration due to Gravity
g = (GE⋅mE) / (RE2)
Velocity of Earth
VE= 4/3πRE2 = 1.08⋅1021 m3
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) / (RE2)
[if the body stays close to Earth]
Speed of the Satellite
v = √(G⋅mE / r)
Period of Circular Orbit
T = (2πr / v)
T = 2πr3/2/√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 = (mv2 / RE)
 
w = w0 - (mv2 / RE)
freefall accele­ration
g = g0 - (v2/ RE)
Black Holes
P = Density
P = M / v
v = 4/3πR3
c = speed of light in the vaccum
Schwar­dzs­child Radius
Rs = 2GM / c2
c = √2GM / RS
 

Chapter 7: Potential Energy, Energy Conser­vation

Y-axis
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 = 1/2kx2
Work Done a Spring
W = 1/2kx22 - 1/2kx12
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) - (b2 / 4m2)
Force Oscill­ations and Resonance
Fmax = Maximum Driving Force
k = constant restoring force
wd = Driving Angular Frequency
A = Fmax / √(k-mwd2)2 + b2wd2
   
 

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