mechanics
velocity
v=
v=
∆s
∆t
ds
dt
acceleration
a=
a=
∆v
∆t
dv
dt
equations of
motion
v = v0 + at
s = s0 + v0t + ½at2
v2 = v02 + 2a(s − s0)
v = ½(v + v0)
newton's 2nd
law
∑F = ma
∑F =
dp
dt
weight
W = mg
dry friction
fs ≤ μsN
fk = μkN
centripetal
accel.
ac =
v2
r
ac = − ω2r
momentum
p = mv
impulse
J = F∆t
⌠
J = ⌡F dt
impulsemomentum
F∆t = m∆v
⌠
⌡F dt = ∆p
work
W = F∆s cos θ
⌠
W = ⌡F · ds
work-energy
F∆s cos θ = ∆E
⌠
⌡F · ds = ∆E
kinetic energy
K = ½mv2
K=
p2
2m
general p.e.
⌠
∆U = − ⌡F · ds
F = − ∇U
gravitational
p.e.
∆Ug = mg∆h
efficiency
η=
Wout
Ein
power
P=
P=
∆W
∆t
dW
dt
power-velocity
P = Fv cos θ
P=F·v
angular
velocity
∆θ
ω=
∆t
ω=
dθ
dt
v=ω×r
angular
acceleration
α=
α=
∆ω
∆t
dω
dt
a = α × r − ω2 r
equations of
rotation
ω = ω0 + αt
θ = θ0 + ω0t + ½αt2
ω2 = ω02 + 2α(θ − θ0)
ω = ½(ω + ω0)
torque
τ = rF sin θ
τ=r×F
2nd law for
rotation
∑τ = Iα
∑τ =
dL
dt
moment of
inertia
I = ∑mr2
⌠
I = ⌡r2 dm
rotational
work
W = τ∆θ
⌠
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
angular
impulse
H = τ∆t
⌠
H = ⌡τ dt
angular i.m.
τ∆t = m∆ω
⌠
⌡τ dt = ∆L
universal
gravitation
Fg = −
Gm1m2
r2
r̂
gravitational
field
g=−
Gm
r2
r̂
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∆x
spring p.e.
Us = ½k∆x2
s.h.o.
T = 2π√
m
k
simple
pendulum
T = 2π√
ℓ
g
frequency
f=
1
T
angular
frequency
ω = 2πf
density
ρ=
m
V
pressure
P=
F
A
pressure in a
fluid
P = P0 + ρgh
buoyancy
B = ρgVdisplaced
mass flow rate
qm =
qm =
∆m
∆t
dm
dt
volume flow
rate
qV =
qV =
∆V
∆t
dV
dt
mass
continuity
ρ1A1v1 = ρ2A2v2
volume
continuity
A1v1 = A2v2
bernoulli's equation
P1 + ρgy1 + ½ρv12 = P2 + ρgy2 + ½ρv22
dynamic
viscosity
F
A
F
A
=η
=η
∆vx
∆y
dvx
dy
kinematic
viscosity
ν=
η
ρ
drag
R = ½ρCAv2