MCAT: Equations

(Physics: Electricity) Capacitors

1/C[s] = ΣC[N]; (in series) C[s] = ΣC[N]; (in parallel) C[s]:capacitance of system (F) C[n]: capacitance of individual capacitor (F)

(Physics: Optics) Thin Lens Equation

1/f = 1/o + 1/i (concave and convex lens) 1/f = 2/r (mirror) f: focal length (m) o: object distance (m) i: (virtual or real) image distance (m) r: radius (m) *Convex lenses converge rays on the focal point, a focal length away, across the lens. When an object is further than the focal point of the lens, it produces an inverted, real image on the other side of the lens. When an object is closer than the focal point of the lens, it produces an upright, virtual image on the same side of the lens. *Concave lenses diverge rays on the other side of the lens. When an object is further than the focal length of the lens, it produces a upright, virtual image on the same side of the lens. When an object is closer than the focal length of the lens, it doesn't produce any images. *Flat Mirror reflect rays on the same side of the mirror and has no focal point or infinite focal points. When an object is closer than than the "focal point" of the mirror, it produces a virtual image on the same side of the mirror. *Convex Mirror diverge rays on the same side of the mirror. When an object is further or closer than the focal point of the mirror, it produces a virtual image on the same side of the mirror. *Concave Mirror converge rays on the same side of the mirror. When an object is further than the focal point of the mirror, it produces an inverted, real image on the same side of the mirror. When an object is closer than the focal point of the mirror, it produces an upright, virtual image on the same side of the mirror.

(Physics: Optics) Focal Length (Series)

1/f = Σ1/f[n] f: focal length (m) f[n]: focal length of individual lens (m)

(Chemistry: Atomic) Aufbau Principle (Max Electrons Per Shell)

2n^2 n: shell Fill electron orbitals of the lower energy orbitals first before higher energy orbitals.

(Physics/ Chemistry: Liquid Dynamics) Continuity

A[1]*v[1] = A[2]*v[2] A[1]: region 1 area (m^2) A[2]: region 2 area (m^2) v[1]: region 1 flow velocity (m/s) v[2]: region 2 flow velocity (m/s)

(Physics: Magnetism) Magnetic Field

B = μ[0]*I/2*(π)*r B: magnetic field (T) μ[0]: permeability of free space (1.26x10^-6 m*kg/(s^2)*(A^2) I: current (A) r: radius (m)

(Physics: Electricity) Capacitance

C = Q/V = ε[0](A/d) C: capacitance (F) Q: charge (C) V: voltage (V) ε[0]: permittivity of free space (8.854x10^-12 F/m) A: surface area (m^2) d: distance (m)

(Physics/ Chemistry: Gas Dynamics) Heat Capacity

C[V] = (3/2)*n*R; (constant volume) C[P] = (5/2)*n*R; (constant pressure) C[V]: heat capacitance (J/K) C[P]: heat capacitance (J/K) n: moles of substance (mol) R: ideal gas constant (8.315 J/mol*K)

(Physics: Electricity) Electric Field

E = F[E]/q = k*q/r^2 E: electric field (N/C or V/m) F[E]: electric force (N) k: Coulomb constant (8.988x10^9 N*m^2/C^2) q: charge (C) Q: charge (C) r: distance (m)

(Chemistry: Atomic) Quantum Number (m[s])

Electron Spin Quantum Number (m[s] = +/- 1/2) s orbital (-1/2, 1/2) p orbital (-1/2, 1/2) d orbital (-1/2, 1/2) f orbital (-1/2/ 1/2)

(Chemistry: Atomic) Pauli Exclusion Principle

Electrons cannot have the same quantum numbers or spin in the same orbital. (Each have unique quantum numbers.) Quantum Number Notation: n, l, m[l], m[s]

(Physics: Mechanics) Hooke's Law

F = -k*x F: force (N) k: spring constant (N/m) x: spring deformation/ displacement (m)

(Physics: Magnetism) Lorentz Force

F = q*E + q*v x B = F[E] + F[B] F: force (N) E: electric field (N/C) B: magnetic field (T) v: velocity (m/s) q: charge (C)

(Physics/ Chemistry: Liquid Dynamics) Buoyant Force

F[B] = m*g = p[fluid]*V*g F[B]: buoyant force (N) m: mass (kg) g: gravitational acceleration (9.8 m/s^2) p[fluid]: fluid density (kg/cm^3) V: volume (cm^3) g: gravitational acceleration (9.8 m/s^2)

(Physics: Magnetism) Magnetic Force

F[B] = q*v*B*sin(θ) = q*v x B F[B] = magnetic force (N) q: charge (C) v: velocity (m/s) B: magnetic field θ: angle (degrees)

(Physics: Electricity) Coulomb's Law (Electric Force)

F[e] = k(q[1]*q[2])/r^2 F[e]: electric force (N) k: Coulomb constant (8.988x10^9 N*m^2/C^2) q[1]: charge of object 1 (C) q[2]: charge of object 2 (C) r: distance (m)

(Physics: Mechanics) Kinetic Frictional Force

F[f, kinetic] = μ[k]*F[N] F[f, kinetic]: kinetic frictional force (N), μ[k]: coefficient of kinetic friction, F[N]: normal force (N)

(Physics: Mechanics) Static Frictional Force

F[f, static] = μ[s]*F[N] F[f, static]: static frictional force (N), μ[s]: coefficient of static friction, F[N]: normal force (N)

(Physics: Mechanics) Gravitational Force (Two Objects)

F[g] = G*m[1]*m[2]/r^2 F[g]: gravitational force (N) G: gravitational constant (6.674x10^-11 m^3/kg*s^2) m[1]: mass of object 1 (kg) m[2]: mass of object 2 (kg) r: distance (m)

(Physics: Mechanics) Gravitational Force (Earth)

F[g] = m*g F[g] = gravitational force (N) m: mass (kg) g: Earthly gravitational acceleration (9.8 m/s)

(Physics: Mechanics) Gravitational Force (Parallel to an Inclined Plane)

F[gx] = m*g*sin(θ) F[gx] = parallel gravitational force (N), m: mass (kg) g: Earthly gravitational acceleration (9.8 m/s^2)

(Physics: Mechanics) Gravitational Force (Perpendicular to an Inclined Plane)

F[gy] = m*g*cos(θ) F[gy]: perpendicular gravitational force (N), m: mass (kg), g: Earthly gravitational acceleration (9.8 m/s^2)

(Physics: Mechanics) Newton's Third Law

F[i] = F[N] = F[T] F[i]: incidental force (N), F[N]: normal force (N), F[T]: tensional force (N)

(Physics: Mechanics) Newton's Second Law

F[net] = m*a F[net]: net force (N), m: mass (kg), a: acceleration (m/s^2)

(Physics: Electricity) Conductance and Resistance

G = σ*A/L = I/R R = p*L/A = 1/G G: conductance (/Ω) R: resistance (Ω) σ: conductivity (m/Ω) p: resistivity (Ω*m) L: length of wire (m) A: cross-sectional area (m^2)

(Chemistry: Thermodynamics) Enthalpy

H = E + P*V H: enthalpy (J) E: internal energy (J) P: pressure (atm) V: volume (L)

(Physics: Waves) Intensity (Complex)

I = 2*(π^2)*(v^2)*(a^2)*p*c I: intensity (W/m^2) f: frequency (Hz) p: density of medium (kg/m^3) a: amplitude of wave (m) c: speed of wave (m/s)

(Physics: Waves) Intensity (Simple)

I = P/A I: intensity (W/m^2) P: power (W) A: area (m^2)

(Physics: Electricity) Current

I = Q/t I: current (A) Q: charge (C) t: time (s)

(Physics/ Chemistry: Gas Dynamics) Absolute Temperature

K = °C = 273.15 K: temperature in Kelvin (K) C: temperature in Celsius (°C)

(Physics: Mechanics) Kinetic Energy

KE = (1/2)*m*v^2 KE: kinetic energy (J) m: mass (kg) v: velocity (m/s)

(Physics/ Chemistry: Gas Dynamics) Kinetic Energy (Gas Particle)

KE[avg] = (3/2)*k[b]*T KE[avg]: average kinetic energy (J) k[b]: Boltzmann constant (1.38x10^-23 (kg*m^2)/(K*s^2)) T: temperature (K)

(Physics: Mechanics) Mechanical Advantage

MA = F[out]/F[in] MA: mechanical advantage F[out]: force output (N) F[in]: force input (N)

(Chemistry: Atomic) Quantum Numbers (m[l])

Magnetic Quantum Number (m[l] = integers from -l to +l) s orbital (0) p orbital (-1, 0, 1) d orbital (-2, -1, 0, 1, 2) f orbital (-3, -2, -1, 0, 1, 2, 3)

(Physics: Mechanics) Newton's First Law

Objects in motion or at rest stay in motion or at rest unless acted upon by an outward force, respectively.

(Physics: Waves) Standing Waves

Open Pipe λ = 2*l/n f = v/λ = n*v/2*l Closed Pipe λ = 4*l/n f = v/λ = n*v/4*l λ: wavelength (m) l: length of pipe (m) n: number of antinodes/ loops (n) f: frequency (Hz) v: velocity (m/s)

(Physics: Optics) Lens Power

P = 1/f P: power (/m) f: focal length (m)

(Physics/ Chemistry: Liquid and Gas Dynamics) Pascal's Law

P = F/A F[1]/A[1] = F[2]/A[2] P: pressure (Pa) F: force (N) A: area (m^2) F[1]: force 1 (N) F[2]: force 2 (N) A[1]: area 1 (m^2) A[2]: area 2 (m^2)

(Physics/ Chemistry: Liquid Dynamics) Hydrostatic Pressure

P = P[0] + p*g*h P = p*g*h P: pressure (Pa) P[0]: initital pressure (Pa) p: density (kg/m^3) g: gravitational acceleration (9.8 m/s^2) h: height (m)

(Physics: Electricity) Power

P = VI = V^2/R = (I^2)*R P: power (W) V: voltage (V) I: current (A) R: resistance (Ω)

(Physics: Mechanics) Power

P = W/t = F*d/t = F*v P: power (W) W: work (J) t: time (s) F: force (N) d: displacement (m) v: velocity (m/s)

(Physics/ Chemistry: Gas Dynamics) Van der Waals State

P = {(n*R*T)/(V - n*b)} - {(a*n^2)/(V^2)} P: pressure (Pa) n: moles of substance (mol) R: ideal gas constant (8.315 J/mol*K) T: temperature (K) V: volume (m^3) a: gas constant a, attractive forces (Pa*(m^3)/mol^2) b: gas constant b, volume per mol (L/mol)

(Physics: Optics) Power of Lenses (Series)

P = ΣP[n] P: total power of lenses P[n]: power of individual lens

(Physics/ Chemistry: Gas Dynamics) Ideal Gas Law

P*V = n*R*T P: pressure (Pa) V: volume (m^3) n: moles of gas (mol) R: ideal gas constant (8.315 J/mol*K) T: temperature in Kelvin (K)

(Physics: Mechanics) Potential Energy (Spring)

PE = (1/2)*k*x^2 PE: potential energy (J) k: spring constant (N/m) x: spring deformation/ displacement (m)

(Physics: Mechanics) Potential Energy (Gravitational: Two Objects)

PE = G*m[1]*m[2]/r PE: potential energy (J) G: gravitational constant (6.674x10^-11 m^3/kg*s^2) m[1]: mass of object 1 (kg) m[2]: mass of object 2 (kg) r: distance (m)

(Physics: Mechanics) Potential Energy (Gravitational: Earth)

PE = m*g*h PE: potential energy (J) m: mass (kg) g: gravitational acceleration (9.8 m/s^2) h: height (m)

(Physics/ Chemistry: Liquid Dynamics) Bernoulli's Law

P[1] + (1/2)*p*v[1]^2 + p*g*h[1] = P[2] + (1/2)*p*v[2]^2 + p*g*h[2] P[1]: elevation 1 pressure (Pa) P[2]: elevation 2 pressure (Pa) v[1]: velocity 1 (m/s) v[2]: velocity 2 (m/s) h[1]: height 1 (m) h[2]: height 2 (m) p: density (kg/cm^3) g: gravitational acceleration (9.8 m/s^2)

(Physics/ Chemistry: Gas Dynamics) Boyle's Law

P[1]V[1] =P[2]V[2] P[1]: pressure 1 (Pa) P[2]: pressure 2 (Pa) V[1]: volume 1 (m^3) V[2]: volume 2 (m^3)

(Physics/ Chemistry: Gas Dynamics) Dalton's Law

P[A] = X[A]*P[T] P = ΣP[N] P[A]: individual partial pressure of A (Pa or atm) P[T]: total pressure (Pa or atm) X[A]: mole ratio of A P: total pressure (Pa or atm) P[N]: individual partial pressure (Pa or atm)

(Physics/ Chemistry: Liquid Dynamics) Poiseuille's Law

Q = (ΔP*π*r^4)/(8*η*l) Q: volume flux (m/s) ΔP: change in pressure (kg/cm^3) η: viscosity (Pa*s) r: vessel radius (m) l: vessel length (m)

(Physics: Electricity) Resistors

R[s] = ΣR[n]; (in series) 1/R[s] = Σ1/R[n]; (in parallel) R[s]: resistance of system (Ω) R[n]: resistance of individual resistor (Ω)

(Chemistry: Thermodynamics) Entropy

S = k[b]*ln(Ω) S: entropy (J/K) k[b]: Boltzmann constant (1.38x10^-23 (kg*m^2)/(K*s^2)) Ω: microscopic configurations (n)

(Physics/ Chemistry: Liquid Dynamics) Specific Gravity

SG = p[object]/p[water] SG: specific gravity p[object]: object density (kg/cm^3) p[water]: water density (kg/cm^3)

SI Constants: 1. Causality/ Speed of Light (C) 2. Gravitational Constant (G) 3. Gravitational Acceleration on Earth (g) 4. Ideal Gas Constant (R) 5. Avogadro's Constant (n) 6. Coulomb's Constant (k) 7. Planck's Constant (h) 8. Boltzmann's Constant (k[b]) 9. Rydberg Constant (R[H]) 10. Faraday Constant (F) 11. Permittivity of Free Space (ε[0]) 12. Permeability of Free Space (μ[0]) 13. Mass and Charge of Proton () 14. Mass and Charge of Neutron () 15. Mass and Charge of Electron () 16. Mass and Charge of Photon ()

SI Constants: 1. 2.997x10^8 m/s 2. 6.674x10^-11 N*m^2/kg^2 3. 9.8 m/s^2 4. 8.314 J/mol*K 5. 6.022x10^23 n 6. 8.988x10^9 N*m^2/C^2 7. 6.626x10^-34 J/Hz 8. 1.381x10^-23 (m^2)*kg/(s^2)*K 9. 1.097x10^7 /m 10. 9.649x10^4 A/mol 11. 8.854x10^-12 (A^2)*(s^4)/kg*m^3 12. 1.257x10^-6 kg*m/(A^2)*(s^2) 13. 1.673x10^-27 kg, 1.602x10^-19 C 14. 1.673x10^-27, 0 C 15. 9.109x10^-31 kg, -1.602x10^-19 16. 0 kg, 0 C

SI Derived Units: 1. Area (A) 2. Volume (V) 3. Speed (s) 4. Velocity (v) 5. Force (F) 6. Torque (τ) 7. Work (W) 8. Energy (E) 9. Frequency (f) 10. Density (p) 11. Heat Capacity 12. Gibbs Free Energy 13. Power (P)

SI Derived Units: 1. meters squared (m^2) 2. meters cubed or liters (m^3 = 1000 L) 3. meters per second (m/s) {scalar} 4. meters per second (m/s) {vector} 5. Newtons (N = kg*m/s^2) 6. Newton-Meters (N*m = kg*m^2/s^2) 7. Joules (J = N*m = kg*m^2/s^2) 8. Joules (J = N*m = kg*m^2/s^2) 9. Hertz (/s) 10. mass per volume (kg/m^3 or kg/L) 11. Joule per Kelvin (J/K) 12. kilojoules per mole (kJ/mol) 13. Watts (J/s)

SI Prefixes: 1. peta (P-) 2. tera (T-) 3. giga (G-) 4. mega (M-) 5. kilo (k-) 6. hecto (h-) 7. deca (da-) 8. base (N/A) 9. deci (d-) 10. centi (c-) 11. milli (m-) 12. micro (μ-) 13. nano (n-) 14. pico (p-) 15. femto (f-)

SI Prefixes: 1. 10^15, 1,000,000,000,000,000 2. 10^12, 1,000,000,000,000 3. 10^9, 1,000,000,000 4. 10^6, 1,000,000 5. 10^3, 1,000 6. 10^2, 100 7. 10^1, 10 8. 10^0, 1 9. 10^-1, 0.1 10. 10^-2, 0.01 11. 10^-3, 0.001 12. 10^-6, 0.000001 13. 10^-9, 0.000000001 14. 10^-12, 0.000000000001 15. 10^-15, 0.000000000000001

(Chemistry: Atomic) Quantum Numbers (n)

Shell (n = nonzero integers) s orbital (1) p orbital (2) d orbital (3) d orbital (4)

SI Base Units: 1. Time (t) 2. Temperature (T) 3. Charge (C) 4. Amount (n) 5. Mass (m) 6. Length/ Distance/ Displacement/ Radius/ Diameter (l, x, d, r, etc.) 7. Volume * "Δ" denotes change in unit ** "°" denotes standard conditions or degree in unit

Standard Units: 1. second (s) 2. Coulomb (C) 3. Celsius (°C), Kelvin (K), Fahrenheit (°F) 4. number (n), mole (mol) 5. gram (g) 6. meter (m) 7. liter (L)

(Chemistry: Atomic) Quantum Numbers (l)

Subshell (l = integers from -(n - 1) to (n-1)) s orbital (0), p orbital (-1, 0, 1), d orbital (-2, -1, 0, 1, 2), f orbital (-3, -2, -1, 0, 1, 2, 3)

(Physics: Mechanics) Mechanical Energy

TE = KE + PE E: total mechanical energy (J) KE: kinetic energy (J) PE: potential energy (J)

SI Standard Conditions

Temperature (T): 0 °C = 273.15 K = 32 °F Pressure (P): 1 atm = 101.325 Pa = 760 mmHg = 14.676 psi Moles: 1 mol Volume: 22.4 L

(Physics: Electricity) Charged Capacitor

U = Q^2/C = (1/2)*Q*ΔV = (1/2)*C*(ΔV)^2 U: energy (J) Q: charge (C) C: capacitance (F) ΔV: change in voltage (V)

(Physics: Electricity) Electric Potential Energy

U = k*q[1]*q[2]/r U: electric potential energy (J) k: Coulomb constant (8.988x10^9 N*m^2/C^2) q[1]: charge of object 1 (C) q[2]: charge of object 2 (C) r: distance (m)

(Physics: Electromagnetism) Maxwell's Right Hand Rule

Use your right hand such that: 1. Thumb: Direction of Current (I) 2. Wrapped Fingers: Direction of Magnetic Field (B)

(Physics: Electromagnetism) Fleming's Right and Left Hand Rule

Use your right hand such that: 1. Thumb: Direction of Force (F) 2. Index Finger: Direction of Magnetic Field (B) 3. Middle Finger: Direction of Current (I) *for dynamos: mechanical motion induces current *for protons in a magnetic field or electrons in a motor Use your left hand such that: 1. Thumb: Direction of Force (F) 2. Index Finger: Direction of Magnetic Field (B) 3. Middle Finger: Direction of Current (I) *for motors: current induces mechanical motion *for electrons in a magnetic field or electrons in a dynamo

(Physics: Electricity) Ohm's Law

V = I*R V: voltage (V) I: current (A) R: resistance (Ω)

(Physics: Electricity) Electric Potential

V = U/q = kq/r V: voltage (V) U: electric potential energy (J) q: charge (C) k: Coulomb constant (8.988x10^9 N*m^2/C^2) r: distance (m)

(Physics/ Chemistry: Gas Dynamics) Charles' Law

V[1]/T[1] = V[2]/T[2} V[1]: volume 1 (m^3) V[2]: volume 2 (m^3) T[1]: temperature 1 (K) T[2]: temperature 2 (K)

(Physics: Mechanics) Work

W = F*d*cos(θ) = F*d W: work (J) F: force (N) d: displacement (m)

(Physics: Mechanics) Average Acceleration

a = Δv/Δt a: acceleration (m/s^2), Δv: velocity (m/s), Δt: time (s)

(Physics: Electromagnetism) Speed of Light

c = fλ c: speed of light (299,792,458 m/s ~ 3x10^8 m/s) f: frequency (Hz) λ: wavelength (m)

(Physics: Waves) Frequency, Period, and Wavelength

f = 1/T = v/λ λ = v/f v = fλ f: frequency (Hz) T: period (s) v: velocity (m/s) λ: wavelength (m)

(Physics: Waves) Doppler Effect

f[O] = f[s]*{(v + v[O])/(v + v[S])} f[O]: frequency at observer (Hz) f[S]: frequency at source (Hz) v: velocity of wave (m/s) v[O]: velocity of observer (m/s) v[S]: velocity of source (m/s)

(Physics: Mechanics) Average Jerk

j = Δa/Δt j: jerk (m/s^3), Δa: acceleration (m/s^2), Δt: time (s)

(Physics: Optics) Magnification

m = h[i]/h[o] = d[i]/d[o] m: magnification ratio h[i]: image height (m) h[o]: object height (m) d[i]: image distance (m) d[o]: object distance (m)

(Physics: Optics) Magnification (Series)

m = m[n-1] x m[n] m: total magnification of lenses m[]: magnification of individual lens

(Physical: Mechanics) Inelastic Collisions

m[1]*v[1] + m[2]*v[2] = (m[1] + m[2])*v[f] m[1]: mass of object 1 (kg) m[2]: mass of object 2 (kg) v[1]: velocity of object 1 (kg) v[2]: velocity of object 2 (kg) v[f]: final velocity (m/s)

(Physics: Mechanics) Elastic Collisions

m[1]*v[1i] + m[2]*v[2i] = m[1]*v[1f] + m[2]*v[2f] m[1]: mass of object 1 (kg) m[2]: mass of object 2 (kg) v[1i]: initial velocity of object 1 (m/s) v[1f]: final velocity of object 1 (m/s) v[2i]: initial velocity of object 2 (m/s) v[2f]: final velocity of object 2 (m/s)

(Physics: Optics) Refraction

n = c/v n: index of refraction c: speed of light (3x10^8 m/s) v: velocity in medium (m/s)

(Physics: Optics) Snell's Law

n[1]*sin(θ[0]) = n[2]*sin(θ[2]) n[1]: index of refraction of medium 1 n[2]: index of refraction of medium 2 θ[1]: angle through medium 1 (°) θ[2]: angle through medium 2 (°)

(Physics/ Chemistry: Gas Dynamics) Avogadro's Law

n[1]/V[1] = n[2]/V[2] n[1]: moles of substance 1 (mol) n[2]: moles of substance 2 (mol) V[1]: volume 1 (m^3) V[2]: volume 2 (m^3)

(Physics: Mechanics) Momentum

p = m*v p: momentum (kg*m/s) m: mass (kg) v: velocity (m/s)

(Physics/ Chemistry: Liquid and Gas Dynamics) Density

p = m/V p: density (kg/cm^3) m: mass (kg) V: volume (cm^3)

(Chemistry: Thermodynamics) Heat Transfer

q = m*C*ΔT q: heat (J) m: mass (g) C: heat capacity or specific heat (J/(g*K)) ΔT: change in temperature (K)

(Physics: Mechanics) Average Speed

s = Δx/Δt s: speed (m/s), Δx: distance (m), Δt: time (s)

(Physics: Mechanics) Translational Kinematics

t = t Δx = r*θ v = r*w a = r*α t: time (s) r: radius (m) Δx: linear displacement (m) θ: angular displacement (rad) v: linear velocity (m/s) w: angular velocity (rad/s) a: linear acceleration (m/s^2) α: angular acceleration (rad/s^2)

(Physics: Mechanics) Average Velocity

v = Δd/Δt v: velocity (m/s), Δd: displacement (m), Δt: time (s)

(Physics: Mechanics) Linear Kinematics

v[F] = v[0] + a*t; (no Δx) Δx = (1/2)*(v[0] + v)*t; (no a) Δx = v[0]*t + (1/2)*a*t^2; (no v[F]) Δx = v[F]*t - (1/2)*a*t^2; (no v[0]) v[F]^2 = v[0]^2 + 2*a*Δx; (no t) a: linear acceleration (m/s^2) v[0]: linear initial velocity (m/s) v[F]: linear final velocity (m/s) Δx: linear displacement (m) t: time (s)

(Physics: Mechanics) Angular Kinematics

w[F] = w[0] + α*t; (no θ) θ = (1/2)*(w[0] + w[F])*t; (no α) θ = w[0]*t + (1/2)*α*t^2; (no w[F]) θ = w[F]*t - (1/2)*α*t^2; (no w[0]) w[F] = w[0]^2 + 2*α*θ; (no t) α: angular acceleration (rad/s^2) w[0]: initial angular velocity (rad/s) w[F]: final angular velocity (rad/s) θ: angular displacement (rad) t: time (s)

(Chemistry: Thermodynamics) Gibbs Free Energy

ΔG = ΔH - ΔT*ΔS ΔG: change in free energy in system (J) ΔH: change in enthalpy (J) ΔT: change in temperature (K) ΔS: change in entropy (J/K) -ΔG is spontaneous, +ΔG is not spontaneous

(Chemistry: Thermodynamics) Standard Enthalpy of Transformation

ΔH° = ΣΔH°[products] - ΣΔH°[reactants] ΔH° = ΣΔH°[bonds broken] - ΣΔH°[bonds formed] *coefficients exist in balanced chemical equations **applies to formation/ deformation, phase change, etcetera ΔH°: standard enthalpy (J)

(Chemistry: Thermodynamics) Expansion

ΔL = α*L*ΔT; (linear expansion: solids) ΔV = β*V*ΔT; (volumetric expansion: solids and liquids) ΔL: change in length (m) ΔV: change in volume (m^3 or L) ΔT: change in temperature (°C) L: length (m) V: volume (m^3 or L) α: expansion coefficient 2 β: expansion coefficient 1

(Physics: Electricity) Electric Potential Difference (Voltage)

ΔV = V[b] - V[a] = W[ab]/q ΔV: voltage (V) V[a]: electrical potential a (V) V[b]: electrical potential b (V) W[ab]: work over ab (J) q: charge (C)

(Physics: Mechanics) Center of Mass

Σm[n]*x[n]/Σm[n] m[n]: mass at point n (kg) x[n]: linear position at point n (m)

(Physics: Waves) Sound Level

β = 10*log[10](I/I[0]) = 1-*log[10](P/P[0]) β[f] = β[i] + 10log[10](I[f]/I[i]) β and β[f]: sound level (dB) I: measured intensity (W/m^2) I[0]: reference intensity (W/m^2) *Reference intensity for human hearing: 1x10^-12 W/m^2

(Physics: Optics) Reflection

θ[Incident] = θ[Reflected] θ[Incident]: incident angle of light (°) θ[Reflected]: reflected angle of light (°)

(Physics: Optics) Critical Angle

θ[c] = sin^-1(n[2]/n[1]) θ[c]: critical angle (°) n[1]: index of refraction of medium 1 n[2]: index of refraction of medium 2 *critical angle is angle for 90° refraction

(Physics: Electromagnetism) De Broglie's Law

λ = h/m*v E = h*f λ: wavelength (m) h: Planck's constant (6.626x10^-34 J*Hz) m: mass (kg) v: velocity (m/s) E: energy (J) f: frequency

(Physics: Mechanics) Torque

τ = r*F*sin(θ) τ: torque (N*m) F: force (N) r: radius (m)