Formulas

final velocity

v_f² = v₀ + 2aΔx

torque

T = rFsinθ

work

W = Fdcos(θ)

work-energy theorem

W_net = ΔKE

power

ΔE/ΔT

units of power

watt = J/s = (kg*m²)/s³

impulse

FΔt = Δp (change in momentum)

center of mass

x_cm = (x₁m₁ + x₂m₂) / (m₁ + m₂)

angular velocity

w = Δθ/Δt

1 revolution

π r

change in the rotation angle

Δθ = Δs/r

moment of inertia

I = mr²

centripetal acceleration

a_c = v²/r

net force in circular motion

F_net = ma_c

Newton’s law of universal gravitational force

F_g = GMm/r²

spring constant

k

Hooke’s law

F_x = -kx

spring potential energy

U = (1/2)kx²

period of a simple harmonic oscillator

T_S = 2π sqrt(m/k)

frequency of a simple harmonic oscillator

f = (1/2π) sqrt(k/m)

angular frequency

w = 2π/T = sqrt(k/m)

amplitude variable

A

max speed

v_max = Aw

max acceleration

a_max = Aw²

period of a simple pendulum

T_p = 2π sqrt(L/g)

position function for simple harmonic motion (w)

x = Acos(wt)

position function for simple harmonic motion (f)

x = Acos(2π ft)

wavelength

λ = v/f

speed of a wave in a string

v = sqrt(T/μ)

mass per unit length of a string

μ = m/L

intensity of sound

dB = 10 log₁₀(I₁/I₀)

beat frequency

f_beat = |f₁ - f|

fundamental frequency

f = V/2L

harmonic frequency from a string attached at both ends

f = nv/2L

harmonic frequency from a pipe open at both ends

f = nv/2L

harmonic frequency of a pipe open at ONE end

f = nv/4L

pressure

P = F/A

liquid pressure

P = P₀ + pgh

buoyant force

F_b = pVg

Archimedes principle

F_b = pV_subg = pV_disg

specific gravity

S.G. = p_obj/p_water

stress

σ = F/A (force/area)

Young’s modulus

y = σ/ε (stiffness = stress/strain)

work done by gas

W = PΔV

first law of thermodynamics

ΔU = Q + W (change in internal energy = heat transferred + work transferred)

conduction

Q = KAΔT/Δx

average kinetic energy of the molecules of a gas

K_avg = (3/2)K_BT

linear thermal expansion

ΔL = aL_iΔT

internal energy

E_internal = sum KE + PE

rate of heat transfer

Q/t = kAΔT/L

momentum of a photon

p = h/λ

total current when resistors are in series

I₁ = I₂ = I₃ (current is the same through each resistorr)

total voltage when resistors are in series

V_total = V₁ + V₂ + V₃

total resistance when resistors are in parallel

1/R_total = 1/R₁ + 1/R₂ + 1/R₃

total current when resistors are in parallel

I_total = I₁ + I₂ + I₃

voltage across resistors in parallel

V₁ = V₂ = V₃ (voltage across each resistor is the same)

index of refraction

n = c/v

Centripetal force

F_c = mv²/r

Angular momentum

L = Iω (momentum of inertia * angular velocity)

Centripetal force sum

F_c = F_G + F_T

Alpha decay

mass number: -4

atomic number: -2

Beta decay

mass number: same

atomic number: +1

Gamma decay

mass number: same

atomic number: same

Energy dissipated by a resistor

Energy = Power * Time

Electrical power formulas

P = IV = I²R = V²/R

Speed of sound given temperature

v = 331 + 0.61*T

index of refraction

n = c/v

Radius of curviture

R = 2f

Lens power

P = 1/f

Wave equation

y = Asin(kx +- wt)

Wave number

k = 2π/λ

negative d_i

virtual image

positive d_i

real image

negative focal point

diverging lens / convex mirror

negative M

inverted

SG is equal to

% of object submerged in fluid

higher index of refraction bends:

away from the normal (horizontal)

lower index of refraction bends:

towards the normal (horizontal)

Absolute pressure

P = P_atm + P_fluidgh

atmospheric pressure = 100,000

Guage pressure

P_g = p_fluid*g*h

isobaric process

pressure remains constant

sin(30)

1/2

sin(45)

sqrt(2)/2

sin(60)

sqrt(3)/2

Work done in moving a charge through a potential difference

W = -qΔV

Angular frequency

w = sqrt(k/m)

Electric potential due to multiple charges:

V = sum (KQ_i/R_i)

K = 1/4πε₀

Pressure under a fluid

P_atm + p_wgh_w

Charge on a capacitator

Q = CV

Total capacitance in a series

C_T = (C₁C₂) / (C₁ + C₂)

Charge on each capacitor in a series

Q_T = Q₁ = Q₂

Kinematic equation to find maximum height of projectile object

v_y² = v_0y² + 2aH_max

Equations for resistance

R = ρl/A

ρ = resistivity

Displacement

Δx = Δx₀ + v_it + (1/2)aΔt²

Final velocity

v_f² = v_i² + 2aΔx