MCAT Physics > Reference Guide

# Physics Reference Guide

## Background

## Standard Units & Variables

### Vectors

- Velocity (v) = m/s
- Acceleration (a) = m/s
^{2} - Displacement (x) = m
- Force (F) = N
- Weight (W) = N
- Momentum (p) = Ns
- Electric Fields (E) = N/C
- Magnetic Field (β) = Tesla (T)
- Torque (τ) = Nm
- Impulse (J) = Ns
- Angular Frequency (ω) = Nms

### Scalars

- Area (A) = m
^{2} - Electric Potential (V) = V
- Time (t) = s
- Current (i) = Amps (a) = C/s
- Mass (m) = kg
- Resistance (R) = ohms (Ω)
- Distance (d) = m
- Capacitance (C) = farad (f) = C/V
- Speed (s) = m/s
- Charge (q) = C
- Length (L) = m
- Volume (V) = g/ml
^{3} - Density (ρ) = kg/L
^{3} - Pressure (P) = Pa
- Temperature (T) = °C or K
- Energy (E) = J
- Work (W) = J
- Heat (Q) = J
- Kinetic Energy (KE) = J
- Potential Energy (PE/U) = J
- Power (P) = watts (w) = J/s
- Wavelength (λ) = m
- Frequency (f) = Hertz (Hz)
- Period (T) = s
- Radius (r) = m
- Entropy (S) = J/K

### Constants

- Acceleration of Gravity (g) = -10 m/s
^{2} - Gravitational Constant (G)= 6.67 x 10
^{-11}Nm^{2}Kg^{-2} - Coulomb's Constant (k) = 9.0 x 10
^{9}= (πε_{0})/4 Nm^{2}C^{-2} - Permittivity of Free Space (ε
_{0}) = 9.0 x 10^{-12}C^{2}N^{-1}m^{-2} - Permittivity of Free Space (μ
_{0}) = 4π x 10^{-7}TmA^{-1}= 1.2 x 10^{-6}T - Avogadro's Number (NA) = 6.022 x 10
^{23} - Stefan-Boltzmann Constant (σ) = 5.67 x 10
^{-8}Wm^{-2}K^{-4} - Gas Constant (R) = 8.31 JK
^{-1}mol^{-1} - c
_{H20}= 4200J - 1.0 x 10
^{5}Pa = 1 atm = 760 torr = 760 mmHg - Speed of Light in a Vacuum (c) = 3.0 x 10
^{8}m/s - Planck's Constant (h) = 6.63 x 10
^{-34}Js - Mass of a Proton = 9.0 x 10
^{-31}Kg - Mass of a Neutron = 1.7 x 10
^{-27}Kg - Mass of an Electron = 1.7 x 10
^{-27}Kg - Elementary Charge (q) = 1.6 x 10
^{-19}C - TC = TK – 273

**Vectors & Kinematics**

v_{f} = v_{i} + at

a = Δv/Δt

a_{X} = 0

d = vit + ½at^{2}

x_{f} – x_{i} = v_{i}xt + ½a_{x}t^{2}

y_{f} – y_{i} = v_{i}yt + ½a_{y}t^{2}

v_{f}^{2} = v_{i}2 + 2a(df – di)

v =(v_{i} + v_{f})/2

Δd = vt = ((v_{i} + v)/2) t

**Forces and Mechanics**

ΣF = ma = 0

W = Fg = mg

F = G (m_{1} m_{2})/r^{2}

τ = rFsinθ

Counterclockwise (+) / Clockwise (−)

F_{c} = ma_{c} = (mv^{2})/r

a_{c} = v^{2}/r

ω = v/r

T = 2πr/v

0 < f_{s} < μ_{s}F_{n}

f_{k} = μ_{k}F_{n}

**Energy**

W = Fd = Fdcosθ = KE = ½mv^{2} = PE = mgh

ΔE_{total} = ΔPE + ΔKE = constant

P = ΔW/Δt

Σp = Σmv

J = FΔt = Δp

mvai + mvbi = mvaf + mvbf (Elastic & Inelastic)

KEa1 + KEb1 = KEa2 + KEb2 (Elastic)

mvai + mvbi = (ma + mb)vf (Inelastic)

Mechanical Advantage = AMA = F_{out}/F_{in}

TMA = d_{1}/d_{0}

Efficiency = AMA/TMA = W_{out}/W_{in} = ((load)(load distance))/((load)(load distance)) x 100

Center of Mass (x)= (m_{1}x_{1} + m_{2}x_{2} + m_{3}x_{3})/(m_{1} + m_{2} + m_{3})

**Thermodynamics**

ΔL = αLΔT (Solids)

ΔV = βVΔT (Gases)

β = 3a

ΔU = Q – W

W = Q = mcΔT = mL = PΔV

ΔS = Q/T

**Substances**

ρ = m/V

W = mg = ρVg

P=F/A ΔP =F_1/A_1 =F_2/A_2 Expands (+) / Compressed (−)

V = A1d1 = A2d2

W = PΔV = F1d1 = F2d2

|P| = Ps + ρgh 1.0x105Pa = 1atm = 760torr = 760mmHg

Pg = P – Patm = (Ps + ρgh) – Patm

FB = ρfVfluid displacedg = ρoVobject submergedg

v_c =(N_r η)/ρD

vA = V/Δt

v1A1 = v2A2 = a constant Acircle = πr2 = (πd^2)/4

|P1|+ ((ρv_1^2)/2)+ ρgy_1 = |P2|+ ((ρv_2^2)/2)+ ρgy_2 = constant

Specific Gravity = ρ1/ρ2

Y =(F/A)/(ΔL/L )=stress/strain

S =(F/A)/(x/h)=stress/strain

B =(F/A)/(ΔV/V)=stress/strain

**Electrostatics**

F =k ((q_1 q_2 ))/r^2 = Eq k = 9.0 x 109 = (πε_0)/4

E =F/q_o = k(q/r^2 ) Repulsion (+) / Attraction (−)

U = k(qQ/r)= W = Fd = Fr

V =k(Q/r)=E/q_0 =W/q_0

W = Vq = VIt = I2Rt

V = (k qd/r^2 )(cosθ)

E = (1/(4πε_0 ))(p/r^3 ) ε0 = 9.0 x 10-12

τ = (qd)Esinθ

**Magnetism**

B =(μ_0 i)/2πr μ0 = 1.2 x 10-6 T Straight Wire

B =(μ_0 i)/2r Circular Wire

F = qvBsinθ = (mv^2)/r Moving Charge

v=L/∆t

F = iLBsinθ Current Carrying Wire

**Circuits**

i =Δq/Δt 1C = 1.0 x 10-19

R =ρL/A

ΣV = ΣiR

P = iV = i^2 R =V2/R=E/ΔT

Rs = R1 + R2 + R3 Vs = V1 + V2 + V3

1/R_p =1/R_1 +1/R_2 +1/R_3 Vp = V1 = V2 = V3

C =Q/V=ε_0 (A/d)

U = ½CV2

E =V/d

C' = KC

1/Cs=1/C1+1/C2+1/C3 Vs = V1 + V2 + V3

Cp = C1 + C2 + C3 Vp = V1 = V2 = V3

i = Imaxsin(2πft) = Imaxsin(ωt) ω = 2πf

I_rms=I_max/√2=V_rms/R

V_rms =Vmax/√2= I_rms R √2 = 1.4

Pmax = Imax2R

Prms = ½Pmax

**Motion and Sound**

Fs = -kxs

as = −ω2ds

ωs = 2πf = 2π/T = √k/m 1 radian = 〖180〗^°/π

PEs = ½kx2

xs = Xcos(ωt)

Fp = -mgsinθ

ωp = 2πf = √g/L

T =1/f=2π/ω

v = fλ = ω/k = λ/T

f =λ/t

vair = 340 + 0.6T Speed of Air = 330

β=10 log(I_f/I_i )

β_f=β_i+10 log(I_f/I_i )

fbeat = |f1 – f2|

f' = f [(v±v_d)/(v±v_s )]

λ =2L/n Strings & Open Pipes

λ =4L/n Closed Pipes, n = odd

**Light and Optics**

c = fλ

θ1 = θ2

1/o+1/i=1/f=2/r Real (+)/Virtual (−)

m = -i/o Upright (+)/Inverted (−)

n =c/v

n1sinθ1 = n2sinθ2

sinv_c =n_2/n_1

1/f= (n – 1)[(1/r_1 )-(1/r_2 )] Non-negligible lens thickness

asinθ = nλ Dark Fringes, n = 1,2,3…

dsinθ = mλ Maxima of Interface, m = 0,1,2,3…

dsinθ = λ(m + ½) Minima of Interface, m = 0,1,2,3…

Convex Mirror/Concave Lenses = upright, inverted, smaller & behind mirror

f=1/D_o +1/D_i f= -1/2 r_c

Concave Mirror/Convex Lenses = real, inverted, in front of or virtual, upright, behind

f= +1/2 r_c

d_i= d_o (-D_i/D_o )

**Atomic Physics**

λpeakT = Constant

ET = σT4 σ = 5.67x10-8

E = hf h = 4.14x1015

λ =c/f c = 3.0x108

v = λf

KE = hf – W

W = hfT

E = -R_H/n^2 RH = 2.18x10-18

E_n = -13.6eV/n_2

**Nuclear Physics**

1 amu = 1.6 x 10-24 g

Alpha (α) Decay = (_Z^A)X→ (_Z-2^(A-4))Y+ α

Beta (β) Decay = (_Z^A)X→ (_Z+1^A)Y+ β- = (_Z^A)X→ (_Z-1^A)Y+ β+

Gamma (γ) Decay = (_Z^A)X→ (_Z^A)Y+ γ

n = n0e-λt

e = 2.70

λ=ln2/T_½ =0.70/T_½