Equations and Trig Function Values
v2
ar =
r
"x = vt + 12 at 2
r dpr
r
F=
" ma
dt
K " 12 mv
2
!
!
!
r r r r
W = # F " ds $ F " %s = Fscos& = %K
r
r
p " mv
r
J=
I = " mi ri
r
r
r
" F dt # F$t = $p
I = " mi ri
!
2
U = mghN kx
!
2
!
SHM " = 2#f = 2# /T
Elastic Collisions
B initially stationary:
!
mA " mB
2mA
k
g
mgd
vA 2 =
v A1
vB 2 =
v A1
"=
"=
"=
mA + mB
mA + mB
m
L
I !
!
Fluids – at rest p = p0 + "gh
CM Frame:
Bernoulli p + "gy + 12 "v 2 = const.
v A 2 = "v A1
v B 2 = "v B1
!
!
!
!
Waves
!
Universal gravitation
y = Acos(kx ± "t)
!
Gm m
GMm
k = 2" / # " = 2# /T
F = !12 2 , U = "
r
r
Kepler T 2 " r 3
T
v=" = 0
!
k
µ
!
!
!
!
!
Rod:
Icm = 121 ML2 Iend = 13 ML2
Solid Sphere: Icm = 25 ML2
r
mi ri
"
r
rcm =
" mi
1
2
2
!
!
Par Axis Thm: I = Icm + Md 2
!
Rotation/
Translation
!
Analogues
"
ω
α
τ
L
I
x
v
a
F
p
m
sin 30° = cos60° =
1
2
cos 30° = sin60° =
3
2
sin 45° = cos 45° =
2
2