- 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 = ma
∑F = dp
dt
- Weight W = mg dry friction ƒ ≤ μN centripetal accel.
ac = v2
r
ac = − ω2r momentum p = mv impulse J = F̅Δt
J = ⌠
⌡ F dt
- Impulse-momentum F̅Δt = mΔv
⌠
⌡ F dt = Δp
- Work
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
η = Wout
Ein
- Power
P̅ = ΔW
Δt
P = dW
dt
- Power-velocity P̅ = F̅v cos θ 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 = Iα
∑ 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 = Iω 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
- Escape speed
v = √ 2Gm
- Hooke's law F = − kΔx elastic p.e. Us = ½kΔx2 s.h.o.
T = 2π √ m
k
- Simple pendulum
T = 2π √ ℓ
- kinematic viscosity
ν = η
ρ
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
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