MCAT Physics Equation Lists (Formulas)

Воскресенье, 10 Июня 2012 г. 02:12 + в цитатник

Memorize These!

Translational motion	x = x ₀ + v ₀ t + 1/2at²	V_ƒ = V_o + at
Frictional force	f _max = μ Ν	μ_k < μ_s always
Uniform circular motion	F_c = ma_c = mv² /r	a_c= v² /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 = mc²
Spring Force, Work	F = -kx	W = kx² /2
Continuity (fluids)	A v = const.	ρAv = const.
Current and Resistance	I = Q/t	R = ρl/A
Resistors (series, par.)	R_eq = R₁ + R₂ . . .	1/ R_eq = 1/ R₁ +1/ R₂
Sound	dB = 10 log ₁₀ (I/I₀ )	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	L₁ = F₁× r₁ (CCW + ve)	L₂ = F₂ × r₂ (CW -ve)
Torque force at EQ	ΣF_x = 0 and ΣF_y = 0	ΣL = 0
Refraction	( sin θ₁ )/(sin θ₂ ) = v₁ /v₂ = n₂ /n₁ = λ₁ /λ₂	n = c/v

Memorize as Pairs

F = ma	F = qE	Similar Form
F = K_G ( m₁ m₂ / r² )	F = k ( q₁ q₂ / r² )
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 mv²	E_p = mgh	(kin, pot E)
Ρ = F/A	Δ Ρ = ρgΔh	(pressure Ρ)
SG = ρ substance / ρ water	ρ = 1 g/cm³ = 10³ kg/m³	(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 ρv² = constant	Bernouilli's Equation	Fluids in Motion
L = L₀ (1 + αΔ T )	Linear Expansion	Solids, Temp Δ
A = A₀(1 + γΔ T )	Area Expansion
V = V₀(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/ C₁ + 1/ C₂ + 1/ C₃ . . .	Capacitors in Ser. and Par.	C_eq = C₁ + C₂ . . .
Potential Energy ( PE ) = W = 1/2 QV	Work in Electricity	W = 1/2 CV²
ΔG = ΔH - TΔS	Gibbs Free Energy	ΔG° = -RTln K_eq

Atomic Physics

1) alpha (α) particle = ₂He⁴ (helium nucleus);

2) beta (β) particle = _-1e⁰ (an electron);

3) a positron ₊₁e⁰ (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 half-lifes 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 n² , 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), n-1, 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^-1θ	r² = x² + y²

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
cross-sectional area of a tube = area of a circle = πr² 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 foot-pound , CGS units: the dyne-centimeter 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/m² ). Other units are: 1.00 atm = 1.01 × 10⁵ 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) = 10⁴ gauss.