Physics 101 Formulas

Kinematics
v_ave = Dx/Dt          a_ave = Dv/Dt
v = v₀ + at                 x = x₀ + v₀t + ¹/₂at²         v² = v₀² + 2aDx
g=9.81m/s² = 32.2ft/s² (near Earth’s surface)

Dynamics
SF = ma                 F_g = Gm₁m₂ / R²     F_g = mg (near Earth’s surface)
f_s,max = m_sF_N           Gravitational constant, G = 6.7 x 10^-11 N.m²/kg²
f_k = m_kF_N a_c = v² / R = w²R

Work & Energy
W_F = FScos(q)        KE = ¹/₂mv²      W_NET = DKE = KE_f - KE_i
W_nc = DE = E_f - E_i = (KE_f + PE_f) - (KE_i + PE_i)
W_grav = -mgDy PE_grav = mgy

Impulse & Momentum
Impulse I = F_aveDt = Dp F_aveDt = Dp = mv_f - mv_i F_ave = Dp/Dt
SF_extDt= DP_total  = P_total,final- P_{total,initial} (momentum conserved if SF_ext = 0)
X_cm = (m₁x₁+ m₂x₂)/ (m₁+m₂)

Rotational Kinematics
w = w₀ + at               q = q₀ + w₀t + ¹/₂at² w² = w₀² + 2aDq
v_T = wR    a_T = aR   ( so for rolling without slipping v = wR    a = aR )

Rotational Statics & Dynamics
t = Fr sin q
St = 0 and SF=0  (static equilibrium)
St = Ia
I = Smr² (for a collection of point particles)
I = ¹/₂MR² (solid disk or cylinder)   I = ²/₅MR² (solid sphere)  I = ²/₃MR² (hollow sphere)
I = MR² (hoop or hollow cylinder)  I = ¹/12 ML² (uniform rod about center)
W = tq (work done by a torque)
L =Iw St_extDt = DL (angular momentum conserved if St_ext = 0)
KE_rot=¹/₂Iw² =L²/2I KE_total=KE_trans + KE_rot = ¹/₂mv² + ¹/₂Iw ²

Simple Harmonic Motion
Hookes Law:  F_s = -kx
W_spring = ¹/₂kx_i² - ¹/₂kx_f² PE_spring = ¹/₂kx²
x(t) = Acos(wt)   or   x(t) = Asin(wt)
v(t) = -Awsin(wt)   or   v(t) = Awcos(wt)
a(t) = -Aw²cos(wt)   or   a(t) = -Aw²sin(wt)
w² = k/m,  T = 2p/w, f = 1/T
x_max= A        v_max = wA    a_max= w²A
For a simple pendulum  w ² = g/L

Fluids
P₂ = P₁ + rg(y₁-y₂)  change in pressure with depth
Buoyant force F_B = rgV_dis = weight of displaced fluid
Flow rate Q = v₁A₁ =  v₂A₂      continuity equation   (area of circle A = pr²)
P₁ + ¹/₂rv₁² + rgy₁ = P₂ + ¹/₂rv₂² + rgy₂    Bernoulli equation
r_water = 1000 kg/m³ 1m³ = 1000 liters
r = M/V 1 atmos. = 1.01 x 10⁵ Pa

Temperature and Heat
temperature:
Celsius (T_C) to Fahrenheit (T_F) conversion: T_C=(5/9)*(T_F-32)
Celsius (T_C) to Kelvin (T_K) conversion: T_K=T_C+273
DL = aL₀DT       DV = bV₀DT      thermal expansion
a_aluminum = 23 x10^-6 and a_steel = 12 x10^-6 (linear expansion coefficients)
Q = cMDT  specific heat capacity
c_water = 4186 J/kg/^oC c_ice = 2000 J/kg/^oC
c_aluminum = 900 J/kg/^oC c_steel = 450 J/kg/^oC
Q = L_fM   latent heat of fusion           Q = L_vM   latent heat of vaporization
L_f,water = 33.5 x10⁴ J/kg     L_v,water = 22.6 x10⁵ J/kg
Q = kADTt/L   conduction
k_steel = 14 J/s/m/^oC k_aluminum = 240 J/s/m/^oC  (thermal conductivities)
Q = esT⁴At      radiation      (s = 5.67x10^-8 J/s/m²/^oK⁴)
P_net = esA(T⁴-T₀⁴)            (surface area of a sphere A = 4pr² )

Ideal Gas & Kinetic Theory
N_A=6.022 x 10²³   molecules/mole        Mass of carbon-12 = 12.000u
PV = nRT = Nk_BT      R = 8.31 J/mol/K      k_B = R/N_A = 1.38 x 10^-23 J/K
KE_ave = ³/₂k_BT = ¹/₂mv_rms²     U =  ³/₂Nk_BT (internal energy of a monatomic ideal gas)
v_rms²   =  3k_BT/m   =  3RT/M  (M = molar mass = kg/mole)

Thermodynamics
DU = Q + W  (1'st law)

U = (³/₂)nRT (internal energy of a monatomic gas for fixed n)

C_V = (³/₂)nR = 12.5 J/^oC/mol (specific heat at constant volume for a monatomic gas)

Q_H = Q_C + W  (heat engine or refrigerator)
e = W/Q_H = 1 - Q_C/Q_H e_max = 1 - T_C/T_H (Carnot engine)
Q_C/Q_H = T_C/T_H   when efficiency is maximum (2'nd law)
W = -PDV  (work done by expanding gas)

Harmonic Waves
v = l / T = l f
v² = F/(m/L)  for wave on a string
v² = 1.4k_BT/m for sound
v = c = 3 x 10⁸ m/s  for electromagnetic waves (light, microwaves, etc.)
I = P / (4pr²)  (sound intensity)

Sound Waves
loudness: β=(10 dB) log₁₀ (I/I₀), where I₀=10^-12 W/m²
(Doppler effect)