Formulas
(you need very few of these!!)
!
xf !
1 2
!
1
2
x = x0 + v0 t + ax t D = CρAv W = ∫! F (x)⋅ dx
xi
2
2
! !
A ⋅ B = A B cosθ
! !
a × b = a b sin φ ⊥ to both
o
h
! ! !
1!
r = r0 + v0 t + a t 2
2
sin θ =
a
h
! ! !
v = v0 + at
cos θ =
tan θ =
Ug = mgh
−b ± b 2 − 4ac
x=
2a
o
a
!
!
! ! !
v 2 = v0 2 + 2a (r − r0 )
gx 2
y = (tanθ )x −
2(v0 cosθ 0 )2
!
!
∑ F = ma
! !
W = F ⋅x
vt2
ar =
r
fs = µ s FN , fk = µ k FN
1
Ws = − kx 2
2
KE =
1 2
mv
2
Fs = −kx
P=
dW
dt
sin30° = 0.5 = cos60°,cos30° = 0.866 = sin60° sin 45° = 0.707 = cos 45°
use
g = 10
m
2 ,
sec
C = 2πr
v=
dx
dt
s = θR
tan 45° = 1
A = πr 2
a=
V=
dv
dt
vt = ωR
1
θ = θ 0 + ω 0 t + α t 2 ω = ω 0 + αt
2
4 3
πr
3
Asphere = 4π r2 Acylinder = 2π rh
T=
2π
ω
at = α R
!
!
p = mv
m − m2
v1 f = 1
v
m1 + m2 1i
I = ∑ mi Ri2
Ihoop = MR 2
Irod =
1
ML2
12
∑mx
i
xcm =
i
i
∑m
v2 f
2m1
=
v
m1 + m2 1i
Idisk =
1
MR 2
2
Igeneral = βMR 2
I = Icm + Md 2
! ! !
τ = r × F = rFsin φ
∑ τ = Iα
!
!
! dp!
F=
dt
Isphere =
KE =
2
MR 2
5
1 2
Iω
2
i
i
τ=
L = Iω
dL
dt
P1 = P0 + ρg(y0 − y1 ) P0 +
! GMm ⌢
F= 2 r
r
1 2
ρv + ρgh = const.
2
U=−
GMm
r
Av = const.
x = xm cos(ω 0t + φ ) vx = −ω 0 xm sin(ω 0t + φ ) ax = −ω 02 xm cos(ω 0t + φ )
ω=
g
L
y = y m sin(kx − ω t)
v=
τ
µ
s = sm cos(kx − ω t)
β = (10dB)log
I
I0
I=
Ps
4π r2
G = 6.67 × 10−11
v=
ω λ
=
k T
v=
fobs = fs
B
ρ
v ± vD
v ∓ vs
ω=
k=
k
m
2π
λ
f b = f1 − f2
v s = 330m /sec