MCAT Physics and Math Equations to Remember

Permittivity of free space

"epsilonnot" 8.85x10^-12 F/m Used in capacitance

Beat Frequency

- Sound volume can increase when two slightly different frequencies are produced in proximity Frequency of "increased sound produced: f(beat) = f1 - f2

Static friction

0 =< F(sf) =<mu(s)N F(sf) = Static friction mu(s) = static friction coefficient N = normal force

Conversion factors of common heat units

1 Cal = 1000 cal = 4184 J = 3.97 BTU

Gauss unit

1 Gauss = 1/10000 Tesla

Pascal

1 Pa = 1 N/m^2

Tesla unit

1 T = 1 Ns/mC 1 T = 10000 Gauss

Specific heat of water

1 cal/(gK) or 4.184 J/(gK)

Density of water

1 g/cm^3 = 1000kg/m^3

Equivalence of pressures

1.013x10^5 Pa = 760 mmHg = 760 torr = 1 atm

Capacitance for capacitors in series

1/Cs = 1/C1 + 1/C2 + 1/... - Functions like RESISTANCE and VOLTAGE drops in PARALLEL - Capacitors in parallel must share the same terminal voltage drops, so each gets less voltage, thus stores less charge

Volume equivalencies

1000 liters = 1 m^3 DON'T THINK 1 cm^3 = 1 mL

Unversal gravitation constant

6.67x10^-11 Nm^2/kg^2

Coulomb's Constant (k)

8.99x10^9 Nm^2/C^2 Also "electrostatic constant"

Magnetic field (Current-carrying, infinite wire)

B = (mu0)I/2Pi(r) B = magnetic field (Ns/mC) mu0 = permeability of free space (4pi x 10^-7 Tm/A) I = current (Amperes) r = radius from wire (m)

Magnetic field (center of loop)

B = (mu0)I/2r B = Magnetic field (Ns/mC) mu0 = Permeability of free space (4pi x 10^-7 Tm/A) I = current r = radius @ LOOP CENTER

Doppler effect

BASED ON SCALAR MOVEMENT, NOT RELATIVE MOVEMENT f(prime) = percieved frequency f = initial sound frequency V = sound speed Vo = velocity of observer Vs = velocity of source - TOP SIGN IF OBSERVER, SOURCE MOVING TOWARD OTHER - BOTTOM SIGN IF OBSERVER, SOURCE MOVING AWAY FROM OTHER

Sound level

Beta = 10 log I/Isub0 I = intensity of sound wave (W/m^2) Isub0 = threshold of hearing (1x10^-12 W/m^2) Beta = sound level (dB) - 10x increase in sound level = + 10 dB

Relationship between coefficients of linear, volumentric expansion

Beta = 3alpha Beta = Coeff. of volumetric expansion alpha = Coeff. of linear expansion

Capacitance

C = Q/V C = capacitance (Farad, 1 C/V) Q = charge (coulombs) V = voltage (volts)

Capacitance of a parallel-plate capacitor

C = epsilonnot(A/D) C = capacitance (Farads, C/V) epsilonnot = permittivity of free space (8.85x10^-12 F/m) A = area of common overlap between capacitors (m^2) d = distance between two plates (meters)

Dielectric constants (and capacitance)

Cprime = kappaC Cprime = real capacitance kappa = dielectric constant, can never be less than 1 C = calculated capacitance - Dielectric constants due to materials put BETWEEN capacitor plates - Constants apply to specific materials - Dielectrics INCREASE capacitance

Capacitance for capacitors in parallel

Cs = C1 + C2 + ... - Functions like RESISTANCE and VOLTAGE drops in SERIES - Since voltage drop is constant across parallel circuits, and capacitance DOES NOT RELATE TO CURRENT, ONLY VOLTAGE, capacitance increases

Electric Potential

DIFFERENT FROM ELECTRIC POTENTIAL ENERGY V = U/q V = Electric potential (Volts) U = Electric potential energy q = charge magnitude

Thermal expansion formula (solid)

DeltaL = alphaLDeltaT L = initial length DeltaL = length chage alpha = coeff. of linear expansion DeltaT = temp. change

Change of entropy equation

DeltaS = Q(rev)/T DeltaS = entropy change Q(rev) = heat change in reversible process T = temp. change

Entropy of the universe

DeltaS(universe) = DeltaS(system) + DeltaS(surroundings) > 0

First law of thermodynamics (+ value explanation)

DeltaU = Q - W DeltaU = change in internal energy, (+) = inc. temp., (-) = dec. temp. Q = Heat, (+) = heat into system, (-) = heat out of system W = Work, (+) = work done by system, (-) = work done on system (compression)

Equivalencies of Work

DeltaU = W = FdcosTheta = Fr X 1 = (kQq/r^2)r = kQq/r

Thermal expansion formula (liquid)

DeltaV = BetaVDeltaT V = initial volume DeltaV = volume change Beta = coeff. of volumentric expansion DeltaT = temp. change

Specific gravity

Density of a fluid at 1 atm + 4 deg C SG = rho/(1g/cm^3) Unitless, usefull for determining sink/float

Electric potential energy

Dependent on relative position of one charge with respect to another U = kQq/r U = potential energy (joules) k = Coulomb's constant, 8.99x10^9 Nm^2/C^2 Q = Influencer charge (generates field) q = receiving charge r = distance between charges

Potential difference

Difference in potential between two points DeltaV = Vb - Va = W(ab)/q W(ab) = amount of work to move a charge from point a -> b SPONTANEOUS IF B IS SMALLER THAN A

Perpendicular bisector of the dipole equation (for E field)

E = 1/4PiSigmaNot X p/r^3 Where E = Electric field (N/C or V/m) SigmaNot = perm. free space p = dipole moment (Cm, p = qd) r = distance from dipole bisector

Electric Field Equation

E = Fe/q = kQ/r^2 Where E = Newtons/Coulomb (field strength) Fe = force q = test charge (infinately small mass, + charge) k = 8.99x10^9 Nm^2/C^2 Q = charge w/ real magnitude (creates field) r = radius from charge

Total mechanical energy

E = U + K

Uniform electric field

E = V/d E= electric field strength (V/m or N/C) V = volts (joule/coulomb) d = distance (m)

Work efficiency in simple machines

Efficiency = W(out)/W(in) = (load)(load distance)/(effort)(effort distance)

Conversion between Fahrenheit and Celsius

F = 9/5(C) + 32

Magnetic force on current-carrying wire

F = ILBsinTheta F = Magnetic force (N) I = Current in wire (A) L = Wire length (m) B = Mag. Field (T) sinTheta = angle between L and B CONSIDER WIRE AS MOVING OF POSITIVE CHARGE

Magnetic force on a moving charge

F = qvBsinTheta F = magnetic force (N) q = charge (coulombs) v = velocity, m/s B = Field strength (T, Ns/mC) sinTheta = incident angle

Archimedes' principle

F(buoy) = rhoV(displ)g = rhoV(sub)g

Centripetal acceleration

F(c) = (mv^2)/r

Gravitational force

F(g) = (Gm1m2)/r^2 r = distance between two CENTERS OF GRAVITY/MASS G = universal gravitation constant, 6.67x10^-11 Nm^2/kg^2

Weight of a volume of liquid

F(g) = rhoVg F(g) = weight rho = density V = volume of liquid g = force of gravity

Kinetic friction

F(kf) = mu(k)N mu(k) = kinetic friction coefficient N = normal force

Coulomb's Law

Fe = KqQ/r^2

Dot Product

For scalar quantities (work, etc.) |A||B|cosTheta = A dot B

Cross Product

For vector quantities A X B = |A||B|sinTheta

Pressure

Force per unit area P = F/A SCALAR QUANTITY

Current

I = Q/Deltat I = current (Amperes) Q = charge (coulombs) Deltat = change in time (in seconds)

Temperature and pressure of thermo processes

Isothermal: Q = W Adiabatic: DeltaU = -W Isobaric: NO SPECIAL FORM Isochoric: DeltaU = Q

Kinetic energy

Ke = 1/2mv^2 In JOULES

Gauge pressure

Liquid pressure IRRESPECTIVE of atmospheric pressure P = rhogz

Mechanical advantage

Ma = F(out)/F(in)

Unit of Torque

Newton Meter (Nm) METER FROM RADIUS

Poiseuille's law

ONLY DURING LAMINAL FLOW Q = pi(r^4)DeltaP/8nL Q = flow rate (vol/sec) r = tube radius DeltaP = pressure gradient n = viscocity L = pipe length

Angular frequency

Omega = 2pi(f) = 2pi/T Omega = angular frequency (radians/second) f = frequency (Hz, sec^-1) T = period (seconds) - Degree of "cycling" in sinusoidal waves, degree of position between trough/crest and sign

Pascal's principle

P = F1/A1 = F2/A2 V = A1d1 = A2d2 WORK IS THE SAME W = Fd, d compensates

Power and Ohm's laws

P = IV = I^2R = V^2/R

Power

P = W/T = DeltaE/T JOULES PER SECOND

Work-energy theorem

P = W/t = DeltaE/t P = power (watts) W = work (joules) t = time (seconds) DeltaE = change in energy (i.e. kinetic, etc.) (joules)

Bernoulli's equation

P1 + 1/2rhov^2 + rhogh1 = P2 + 1/2rhov^2 + rhogh2 P = absolute fluid pressure rho = density v = linear velocity g = gravitational accelleration h = height of fluid above a set point (potential energy)

continuity equation (fluids)

Q = v1A1 = v2A2 FLOW RATE IS CONSTANT Q = flow rate v = linear speed A = cross-sectional area

Resistance equation

R = rhoL/A R = resistance rho = resistivity L = length of resistor A = Cross-sectional area of wire

Resistivity

Reistance of a specific material to the movement of electrons SI unit is the Ohm-meter

Density

Rho = m/V

Resistors in series and parallel

SERIES: V(series) = Vdrop1 + Vdrop2 +... R(series) = R1 + R2 +... PARALLEL: Vdrop(parallel) = Vdrop1 = Vdrop2 V = IR, -> I splits, V reacts to I 1/R(parallel) = 1/R1 + 1/R2 + 1/.... - R(parallel) always decreases w/ increasing number of resistors!

Ampere

SI unit of current 1 A = 1 coulomb/second

45 degrees

Sine = (Sq.Rt. 2)/2 Cosine = (Sq.Rt. 2)/2 Tangent = 1

60 degrees

Sine = (Sq.Rt. 3)/2 Cosine = 1/2 Tangent = Sq.Rt. 3

90 degrees

Sine = 1 Cosine = 0 Tangent = Infinity

30 degrees

Sine = 1/2 Cosine = (Sq.Rt. 3)/2 Tangent = (Sq.Rt. 3)/2

Period

T = 1/f

Torque on an electrical dipole

Tau = pEsinTheta Tau = torque (Nm) p = dipole moment (qd) E = Electric field (N/C or V/m) sinTheta = angle of field to dipole

Absolute hydrostatic pressure

Total pressure exerted on object submerged in a fluid P = P(0) + rhogz P(0) = ambient pressure (pressure at surface, atmospheric pressure) rho = density of liquid g = acceleration due to gravity z = depth of liquid

Potential energy stored in a capacitor

U = 1/2CV^2 U = potential energy (joules) C = capacitance (farads, 1 C/V) V = voltage (volts, N/m or J/C

Gravitational potential energy

U = mgh

Siemens unit

Unit of CONDUCTANCE Expressed in materials as Siemens/meter for conductivity

Farad

Unit of capacitance 1 F = 1 C/V

Volts (units)

Units of electric potential NOT ELECTRIC POTENTIAL ENERGY 1 Joule/Coulomb V = kQ/r

Intensity

Usable for light, sound, anything w/ spherical area affect I = P/A ALSO, I = Sq.rt. (Amplitude) I = intensity (W/m^2) P = power (Watts) A = area (m^2) Amplitude in meters - Assuming intensity uniformly distributed, intensity of vibration on a surface (eg. timpanic membrane) can be estimated - Intensity inversely proportional to sq. rt. distance form source

Internal resistance

V = EMF(cell) - Ir(internal) - If the battery isn't driving any current at this time, I = 0, so internal resistance = 0, voltage = EMF

Dipole equation (for equal + opposite dipoles)

V = kqdCosTheta/r^2 V = Voltage, Electric potential k = Coulom's constant, 8.99x10^9 Nm^2/C^2 q = charge d = dipole length cosTheta = angle from dipole center to point of interest r = distance from dipole center to point of interest ONLY WORKS IF d << r Can also be written: V = kpCosTheta/r^2 p = dipole moment

Critical speed formula

V(c) = N(R)n/rhoD V(c) = critical speed N(R) = Reynold's number (dimensionless) n = viscosity rho = liquid density D = tube diameter

Ohm's law

V=IR V is ALWAYS voltage DROP, or EMF Voltage drop is relative to resistance of each resistor, since current is constant in a NON-SPLIT circuit

Isobaric Gas processes

W = PDeltaV

Work-Energy Theorem

W(net) = DeltaK = K(f) - K(i) K = kinetic energy

System energy with and without nonconservative forces

WITHOUT: DeltaE = DeltaU + DeltaK = 0 WITH: W(nonconserv) = DeltaE = DeltaU + DeltaK

Coulomb value

e = 1.6x10^-19 C

Wavelength of a standing harmonic wave IN A STRING

lambda = 2L/n lambda = wavelength L = length of string n = harmonic number (# of nodes -1) IDENTICAL TO OPEN PIPE

Viscosity

n. Resistance of a fluid to flow. PASCAL-SECOND Pa*s, Ns/m^2

Dipole moment equation

p = qd p = dipole moment (Cm) q = charge on one end of dipole (should be identical to other side, but opposite in sign) d = length of dipole (between both points

Phase change heat formula

q = mL q = heat energy m = mass L = Latent heat, heat of transformation

Specific heat formula (not during phase change)

q = mcDeltaT q = heat energy m = mass c = specific heat DeltaT = change in temperature

Torque

tau = r X F = rFsinTheta

Speed of a wave

v (or c) = flambda

Speed of sound (relative to a MEDIUM)

v = Sq.rt.(B/rho) v = speed in m/s B = bulk modulus (resistance to compression, highest in solid, lowest in gas) rho = density of fluid - Bulk modulus increases disproportionately faster than density increases going gas->solid

Linear motion equations

v = v(0) + at x = v(0)t + (at^2)/2 v^2 = v(0)^2 + 2ax x = v(av)t

To find the center of mass, sometimes gravity

x,y,z coordinates of center of mass x = ((x(1)m(1)) + (x(n+1)m(n+1))...)/(m(1) + m(n+1)...) Same for y, z