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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
x
f
+x
i
One Dimens­ional Motion
Distance
d = s⋅t
Displa­cement
x
f
-x
i
Speed
(x
f
+x
i
) / (t
f
+
t
i`)
Not Constant Velocity
Average Velocity
(x
f
-x
i
) / (t
f
-
t
i`)
x↑: v+
x↓: v-
x→: v=0
a+: v↑
a-: v↓
a=0: v→
Instan­taneous Accele­ration
(v
f
-v
i
) / (t
f
-
t
i`)
Constant Accele­ration in 1D
V
f
= V
i
+ (a⋅t)
Constant Accele­ration Final Distance
X
f
= 1/2(V
f
-V
i
) ⋅ t
X
f
= X
i
+ (V
i
⋅ t) + 1/2(a ⋅ t)
a = (V
f
-V
i
) / t
t = (V
f
-V
i
) / a
V
f
= V
i
⋅ a2
V
f
2 = V
i
2 + 2⋅a (x
f
-x
i
)
G
y
= -9.8 m/s

Chapter 14: Periodic Motion

Angular Frequency
w = 2πf
2π/T
Frequency
f = 1 / T
Period
T = 1 / f
Restoring Force
F
x
= -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)
x
max
 = A [Ampli­tude]
-x
max
 = A [Ampli­tude]
v
max
 = wA
-v
max
 = wA
a
max
 = w2A
-a
max
 = 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 = 1/2mv
x
2 + 1/2kx2
 
E = 1/2kA2
 

Chapter 6: Work and Kinetic Energy

1km = 1000m
1 kg = 1000g
Dot Product
P = Power
A⋅B = (A
i
⋅B
i
)+(A
j
⋅B
j
)
t = s
Work = Force ⋅ distance
W = F
x
⋅ distance
W = F⋅cosΘ­⋅di­stance
K
E
: 1/2⋅m⋅v2
U = m⋅g⋅h
W
total
= K
E
f
- K
E
i
W
x
= F (cosΘ)⋅s || W
y
= F (sinΘ)⋅s
Constant Speed
Friction (opposite) = cos(180o)
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
F
x
= k ⋅ x

Chapter 13: Newton's Law of Gravit­ation

G
E
= 6.67⋅10-11
Earth Gravity Constant
R
E
= 6.38⋅106 m
Earth Radius
M
E
= 5.972⋅1024 kg
Mass of Earth
g = 9.8 m/s; a
g
= 9.8 m/s
r - R
E
= h
F
g
= (G
E
⋅m
1
⋅m
2
) / (r2)
F
g
= m ⋅ a
w = m⋅g
s = r - R
E
cosΘ
Gravit­ation and Spheri­cally
Symmetric Bodies
F
g
= (G
E
⋅m
E
⋅m) / (r2)
Weight of the body at Earth's Surface
w = F
g
= (G
E
⋅m
E
⋅m) / (R
E
2)
Accele­ration due to Gravity
g = (G
E
⋅m
E
) / (R
E
2)
Velocity of Earth
V
E
= 4/3πR
E
2 = 1.08⋅1021 m3
Gravit­ational Potential Energy
U = -(G
E
⋅m
E
⋅m) / (r)
WorkDone by Gravity
W
grav
= m⋅g(r
1
-r
2
)
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
v = √(G⋅m
E
/ r)
Period of Circular Orbit
T = (2πr / v)
T = 2πr3/2/√G⋅m
E
T = 2πr √(r / G⋅m
E
)
Point Mass Outside
a Spherical Shell
U
i
= - Gm⋅m
i
/ s
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`
w
0
- F = (mv2 / R
E
)
 
w = w
0
- (mv2 / R
E
)
freefall accele­ration
g = g
0
- (v2/ R
E
)
Black Holes
P = Density
P = M / v
v = 4/3πR3
c = speed of light in the vaccum
Schwar­dzs­child Radius
R
s
= 2GM / c2
c = √2GM / R
S
 

Chapter 7: Potential Energy, Energy Conser­vation

Y-axis
E = Mechanical Energy
W
grav
= F ⋅ s = w(y
1
-y
2
)
W
grav
=(m⋅g⋅y
1
)-(m⋅g⋅y
1
)
W
grav
=U
grav,1
- U
grav,2
W
grav
= -Δ U
grav
Conser­vation
of Mechanical Energy
K
f
-K
i
= U
grav,1
- U
grav,2
K
i
+U
grav,1
=K
f
+U
grav,2
E = K + U
grav
= constant
(if gravity does work)
When other forces
than Gravity do work
W
other
+ W
grav
= K
f
- K
i
Elastic Potential Energy
U
el
= 1/2kx2
Work Done a Spring
W = 1/2kx
2
2 - 1/2kx
1
2
If Elastic does work,
total mechanical energy
is stored
K
i
+U
el,1
=K
f
+U
el,2
Situations with Both Gravit­ational
and Elastic Potential Energy
K
1
+U
1
+W
other
=K
2
+U
2
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
F
x
(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
F
max
= Maximum Driving Force
k = constant restoring force
w
d
= Driving Angular Frequency
A = F
max
/ √(k-mw
d
2)2 + b2w
d
2
   
 

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  • Published: 15th December, 2021

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