


MCAT Physics Equation Lists (Formulas) 
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MCAT Physics Equations to memorize 
Translational motion 
x = x _{0} + v _{0} t + 1/2at^{2} 
V_{ƒ} = V_{o} + at 
Frictional force 
f _{max} = μ Ν 
μ_{k} < μ_{s} always 
Uniform circular motion 
F_{c} = ma_{c} = mv^{2} /r 
a_{c}= v^{2} /r 
Momentum, Impulse 
I = F Δt = ΔM 
M = mv 
Work, Power 
W = F d cosθ 
P = ΔW/Δt 
Energy (conservation) 
E_{T} = E_{k} + E_{p} 
E = mc^{2} 
Spring Force, Work 
F = kx 
W = kx^{2} /2 
Continuity (fluids) 
A v = const. 
ρAv = const. 
Current and Resistance 
I = Q/t 
R = ρl/A 
Resistors (series, par.) 
R_{eq} = R_{1} + R_{2} . . . 
1/ R_{eq} = 1/ R_{1} +1/ R_{2} 
Sound 
dB = 10 log _{10} (I/I_{0} ) 
beats = Δ f 
Kirchoff's Laws 
Σi = 0 at a junction

ΣΔV = 0 in a loop 
Thermodynamics 
Q = mc Δ T (MCAT !) 
Q = mL 
Torque forces 
L_{1} = F_{1}× r_{1} (CCW + ve) 
L_{2} = F_{2} × r_{2} (CW ve) 
Torque force at EQ 
ΣF_{x} = 0 and ΣF_{y} = 0 
ΣL = 0 
Refraction 
( sin θ_{1} )/(sin θ_{2} ) = v_{1} /v_{2} = n_{2} /n_{1} = λ_{1} /λ_{2} 
n = c/v 


MCAT Physics Equations to memorize as pairs 
F = ma

F = qE 
Similar Form 
F = K_{G} ( m_{1} m_{2} / r^{2} ) 
F = k ( q_{1} q_{2} / r^{2} ) 

V = IR 
P = IV 
Paired Use 
v_{av} = Δ d / Δ t 
a_{av} = Δ v / Δ t 
(avg vel, acc) 
v = λ f 
E = hf 
(f = 1/T) 
E_{k} = 1/2 mv^{2} 
E_{p} = mgh 
(kin, pot E) 
Ρ = F/A 
Δ Ρ = ρgΔh 
(pressure Ρ) 
SG = ρ substance / ρ water 
ρ = 1 g/cm^{3} = 10^{3} kg/m^{3} 
(Spec Grav) 
ρ = mass / volume 
F_{b} = Vρg = mg 
(buoyant F) 
I_{rms} = I_{max} / √2 
V_{rms} = V_{max} / √2 
Root Mean Sq 
1/ i + 1/ o = 1/ f = 2/r = Power 
M = magnification =  i/o 
Optics 
Note: Specific gravity (SG) is equivalent to the fraction of the height of a buoyant object below the surface of the fluid. 


Don't Memorize, Know How to Use... 
Ρ + ρgh + 1/2 ρv^{2} = constant 
Bernouilli's Equation 
Fluids in Motion 
L = L_{0} (1 + αΔ T ) 
Linear Expansion 
Solids, Temp Δ 
A = A_{0}(1 + γΔ T ) 
Area Expansion 

V = V_{0}(1 + βΔ T ) 
Volume Expansion 
β = 3 α 
f_{o} = f_{s} (V ± v_{o} )/( V ± v_{s} ) 
Doppler Effect: when d is decreasing use + v_{o} and  v_{s} 

V = Ed for a parallel plate capacitor 
d = the distance between the plates 

dF = dq v(B sin α) = I dl(B sin α) 
Laplace's Law 
RH rule 
1/ C_{eq} = 1/ C_{1} + 1/ C_{2} + 1/ C_{3} . . . 
Capacitors in Ser. and Par. 
C_{eq} = C_{1} + C_{2} . . . 
Potential Energy ( PE ) = W = 1/2 QV 
Work in Electricity 
W = 1/2 CV^{2} 
ΔG = ΔH  TΔS 
Gibbs Free Energy 
ΔG° = RTln K_{eq} 




Atomic Physics 
1) alpha (α) particle = _{2}He^{4} (helium nucleus);
2) beta (β) particle = _{1}e^{0} (an electron);
3) a positron _{+1}e^{0} (same mass as an electron but opposite charge);
4) gamma (γ) ray = no mass, no charge, just electromagnetic energy;
5) Δ m /Δ t = rate of decay where Δ m = change in mass, Δ t = change in time.
6) If the number of halflifes n are known we can calculate the percentage of a pure radioactive sample left after undergoing decay since the fraction remaining = (1/2)^{ n} .
N_{electrons} = 2 n^{2} , where N_{electrons} designates the number of electrons in shell n .
The state of each electron is determined by the four quantum numbers:
 principal quantum number n determines the number of shells, possible values are: 1 (K), 2 (L), 3 (M), etc...
 angular momentum quantum number l, determines the subshell, possible values are: 0 (s), 1 (p), 2 (d), 3 (f), n1, etc...
 magnetic momentum quantum number m_{l} , possible values are: ± l , ... , 0
 spin quantum number m_{s} ,determines the direction of rotation of the electron, possible values are: ±1/2.


The Basics 
sin θ = opp/hyp 
cos θ = adj/hyp 
tan θ =opp/adj 
θ = sin ^{1} x 
arcsec θ = sec^{1}θ 
r^{2} = x^{2} + y^{2} 
 angle θ may be given in radians (R) where 1 revolution = 2π^{R} = 360°
 estimate square root 3 as 1.7 and root 2 as 1.4
 crosssectional area of a tube = area of a circle = πr^{2} where π can be estimated as 3.14 and r is the radius of the circle; circumference = 2πr


Some Units to Memorize 
 Both work and energy are measured in joules where 1 joule (J) = 1 N × 1 m . {Imperial units: the footpound , CGS units: the dynecentimeter or erg }
 The SI unit for power is the watt (W) which equals one joule per second (J/s) = volts × amperes .
 Current is measured in amperes = coulombs/sec. The units of resistance are ohms, symbolized by Ω (omega), where 1 ohm = 1 volt/ampere.
 The SI unit for pressure is the pascal (1 Pa = 1 N/m^{2} ). Other units are: 1.00 atm = 1.01 × 10^{5} Pa = 1.01 bar = 760 mmHg = 760 torr.
 The SI unit for the magnetic induction vector B is the tesla where 1 T = 1 N/(A)(m) = 10^{4} gauss.




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