Some Important Equation of Physics

Mechanics

velocity

v̅ =  Δs Δt

v =  ds dt

acceleration

a̅ =  Δv Δt

a =  dv dt

equations of motion

v = v0 + at x = x0 + v0t + ½at2 v2 = v02 + 2a(x − x0) v̅ = ½(v + v0)

newton's 2nd law

∑ F = m a

∑ F =  dp dt

weight

W = m g

dry friction

ƒ = μN

centrip. accel.

ac =  v2 r

ac = − ω2 r

momentum

p = m v

impulse

J = F̅ Δt

J =  ⌠ ⌡ F dt

impulse-momentum

F̅ Δt = m Δv

⌠ ⌡ F dt = Δp

work

W = F̅Δs cos θ

W =  ⌠ ⌡ F · ds

work-energy

F̅Δs cos θ = ΔE

⌠ ⌡ F · ds = ΔE

kinetic energy

K = ½mv2

general p.e.

ΔU = −  ⌠ ⌡ F · ds

F = − ∇U

gravitational p.e.

ΔUg = mgΔh

efficiency

ℰ =  Wout Ein

power
P̅ =  ΔW Δt	P̅ = F̅v cos θ
P =  dW dt	P = F · v

angular velocity

ω̅ =  Δθ Δt

ω =  dθ dt

v = ω × r

angular acceleration

α̅ =  Δω Δt

α =  dω dt

a = α × r − ω2 r

equations of rotation

ω = ω0 + αt θ = θ0 + ω0t + ½αt2 ω2 = ω02 + 2α(θ − θ0) ω̅ = ½(ω + ω0)

2nd law for rotation

∑ τ = I α

∑ τ =  dL dt

torque

τ = rF sin θ

τ = r × F

moment of inertia

I = ∑ mr2

I =  ⌠ ⌡  r2 dm

rotational work

W = τ̅Δθ

W =  ⌠ ⌡  τ · dθ

rotational power

P = τω cos θ

P = τ · ω

rotational k.e.

K = ½Iω2

angular momentum

L = mrv sin θ L = r × p L = I ω

universal gravitation

Fg = −  Gm1m2  r̂ r2

gravitational field

g = −  Gm  r̂ r2

gravitational p.e.

Ug = −  Gm1m2 r

gravitational potential

Vg = −  Gm r

orbital speed

v = √  Gm r

escape speed

v = √  2Gm r

hooke's law

F = − k Δx

elastic p.e.

Us = ½kΔx2

s.h.o.

T = 2π √  m k

simple pendulum

T = 2π √  ℓ g

frequency

ƒ =  1 T

angular frequency

ω = 2πƒ

density

ρ =  m V

pressure

P =  F A

pressure in a fluid

P = P0 + ρgh

buoyancy

B = ρgVdisplaced

mass flow rate

I =  m t

volume flow rate

φ =  V t

mass continuity

ρ1A1v1 = ρ2A2v2

volume continuity

A1v1 = A2v2

bernoulli's equation
P1 + ρgy1 + ½ρv12 =	P2 + ρgy2 + ½ρv22

dynamic viscosity

η =  F̅/A Δvx/Δz

η =  F/A dvx/dz

kinematic viscosity

ν =  η ρ

aerodynamic drag

R = ½ρCAv2

mach number

Ma =  v c

reynolds number

Re =  ρvD η

froude number

Fr =  v √gℓ

young's modulus

F  = E  Δℓ A ℓ0

shear modulus

F  = G  Δx A y

bulk modulus

F  = K  ΔV A V0

surface tension

γ =  F ℓ