Newtonian
Mechanical energy
ME= KE + PE
Work
W=F d cosӨ
Energy
PE= mgh
Kinetic energy = ½ mv2
Work –Kinetic Energy Theorem
WNET= ∆KE= ½ mv2 f - ½ mvi2
Inelastic collision:
m1v1+m2v2=(m1+m2)vf
Elastic collision
m1v1i+ m2v2i = m1v1f+ m2v2f
ME= Mechanical energy
PE= Potential Energy
KE= Kinetic Energy
m= mass
g= acceleration of an object due to Earth’s
gravitational pull
h= height
d=distance
v= velocity
F=force
Ff=Force of Friction
p= momentum
P=Power
t=time
G= Newton’s Gravitational Constant
 rad/s
Impulse Momentum Theorem
F∆t=m∆v
Vt = tangential velocity
Momentum
p=mv
Δp=F∆t
Δp=m∆v
KE Rotational = Rotational kinetic energy
Power
m= mass
𝑊
P= 𝑡
P = Fvcosθ
Force
F=ma
Fw=mg
Ff= µFn
Newton’s law of gravitation
Fg=
𝐺𝑚1 𝑚2
𝑟2
Gravitational Potential Energy
PE=
𝐺𝑚1 𝑚2
𝑟
Fc = Centripetal Force
𝜏 = Torque
r = radius
α =acceleration
v = velocity
Motion
d= vt
vf = vi+ at
d= vit + ½ at2
vf2 = vi2 + 2ad
d= ½(vi+vf)t
Graphs:
Rotational motion
At = rα
Ac =
𝑣2
𝑟
Fc =mac =
𝑚𝑣 2
𝑟
KE Rotational= ½ 
𝜏 = r Fsinθ
vt = r
Thermodynamics and Gases
Q= Heat energy
3𝑅𝑇
𝑀
Vrms= √
t = time
m= mass
∆l = αL∆T
Thermal Efficiency
Eff =
𝑄𝐻−𝑄𝐶
𝑄𝐻
k = thermal conduction
KB = Boltzman’s constant
A= cross sectional area
Q = mL
TH= Temperature of____
Q= mc∆T
TC = Temperature of _____
PV=nRT
H= Rate of heat transfer
Carnot Efficiency:
T= Temperature
Eff =
𝑇𝐻 −𝑇𝐶
𝑇𝐻
Average kinetic Energy of Gas
3
R = gas constant
L= Length of rod
KE = 2KbT
L= Latent Heat (Q=mL)
Work done by gas
W = Work
W= -P∆V
U= Internal Energy
H=
𝑘𝐴∆𝑇
𝐿
or
ΔU = Q + W
𝑄
𝑡
Fluid Dynamics
Buoyancy
Fbuoy = fluidVsubstance g
Pressure
P=
𝐹
𝐴
1
2
P1 + gy1 + ½ v21 =P2 + gy2 + v22
Pgauge = Ptotal –P atmosphere
Pgauge = gh
Hydrostatic pressure:
𝐹
Pliquid = 𝐴= gh
Specific gravity =
Flow Rate:
A1v1=A2v2
𝜌 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒
𝜌 𝑤𝑎𝑡𝑒𝑟
F= buoyancy force
P = pressure
A= Area
density
g= acceleration due to Earth’s gravitational pull
A= cross sectional area (for flow rate)
v =velocity
y= height
Simple Harmonic motion
Fspring = -kx
v = velocity of stretched string
𝑙
Tpendulum = 2𝜋√𝑔
𝑚
Tspring = 2𝜋√ 𝑘
1
𝑔
fpendulum =2𝜋 √ 𝑙
fspring=
1
𝑘
√
2𝜋 𝑚
m= mass
g= acceleration of object due to Earth’s
gravitational pull
m = mass density
T=period
f= frequency
1
PEspring =2kx2
PE= potential energy
Frestoring = mgsin 𝜃
Vstretched string =
Ft= tension in string
𝐹𝑡
𝜇
F = force
l = length of string
k= spring constant
x= distance from equilibrium point
Waves
f= frequency
T = period
1
f= 𝑇
F𝛽= Sound level
1
= wavelength
T= 𝑓
𝑛𝑣
fn = 4𝐿 n = 1,3,5,…
n= order
4𝐿
𝜆n = 𝑛
v = velocity
2𝐿
𝜆n =
𝑛
fn =
I=
𝑛𝑣
2𝐿
L = length of pipe
n = 1,2,3,…
fbeat = f1-f2
β=10 log
𝐵
𝜌
P= Power
 density
𝑃
4𝜋𝑟 2
v= √
I = intensity
𝐼
𝐼𝑜
Electricity and Magnetism
FB= qvBsin 𝜃
Cparallel = C1 + C2 + C3 …
Cseries =
FB =BILsin 𝜃
1
𝐶1
+
1
𝐶2
+
1
𝐶3
…
PE = ½CV2 = QV
∆∅𝑚

∆𝑡

FB= force produced by magnetic field
= Blv
 EMF or voltage
 = BAcos 𝜃
Q or q = charge
𝜇𝐼
B=
v = velocity
2𝜋𝑟
B = magnetic field
2𝜋𝑚
T=
𝑞𝐵
I = current
𝑞𝐵
f=
2𝜋𝑚
L or l= Length of the rod
FElectric= K
𝑞1 𝑞2
 magnetic flux
𝑟2
𝑉2
P = VI= I2R =
A = area
𝑅
 magnetic permeability
𝑉
R=
𝐼
r =distance
R=
𝜌𝑙
𝐴
R= resistance
Rs = R1 + R2 + R3 …
1
Rp =
I=
+
𝑅1
∆𝑄
∆𝑡
1
𝑅2
𝑉
=
+
1
𝑅3
…
 resistivity
E= electric field
d= distance
𝑅
a= acceleration
V= -Ed
m= mass
I = qnVdA
K= Coulombs constant
WE=qEd
F = Force
𝑞
a= E
𝑚
E=
E=
 x 10-12
𝐹
C = Capacitance
𝑞
𝐾𝑞
𝑟2
C=
∈𝑜𝐴
V = Voltage
P = Power
𝑑
n= number of charge carriers
C=
𝑄
𝑉
Vd= drift velocity
Optics
n = index of refraction
𝑐
n=𝑣
c = speed of light
n1sin 𝜃 1= n2sin 𝜃2
M = Magnification
ℎ
𝑠
M= ℎ 𝑖 =𝑠 𝑖
𝑜
1 1
=
𝑓 𝑞
V= velocity
𝑜
h= height
1
+𝑝
f= focal length
f=
𝑅
2
R = radius of curvature
si = image distance
so =object distance
Atomic and Nuclear Physics
Z= protons
Δ𝑚 = Z(atomic mass of H) + N (mass of
neutrons) – Atomic mass
N= neutrons
E= Energy
E =hf = pc
h= Planck’s constant
Kmax = hf -∅
f = frequency
Xm =
𝑚𝜆𝐿
𝑑
p= momentum
ℎ
𝑚 𝑐cos 𝜃
c= speed of light
∆E=∆mc2
𝜙 = work function
dsin 𝜃 = 𝜆m
Δm = mass defect
v= f𝜆
d= distance between slits
𝑒
𝜆=
ℎ
𝑝
m= order number
𝜆 = wavelength
me = mass of electron