Formula Sheet
1
~r = r~0 + v~0 t + ~at2
2
2
2
vf = v0 + 2~a · ~r
x=
v02
sin 2✓0
g
y = x tan ✓0
v~f = v~0 + ~at
y=
2v02
g
x2
cos2 ✓0
mv 2
F =
r
f s  µs N
F~ = k~x
F~ = m~a
f k = µk N
~ = m~g
W
1
K = mv 2
2
W = F~ · ~r
Z
W = F~ · ~r
K=W
dW
dt
1 2
U = kx
2
d~p
F~ =
dt
vf
1
✓(t) = ✓0 + !0 t + ↵t2
2
! 2 = !02 + 2↵ ✓
Z
W = ⌧ d✓
~⌧ =
@U
ĵ
@y
U = mgh
p~ = m~v
P
mi~ri
~rcm = Pi
i mi
I=
@U
î
@x
F~ =
P =
Z
v02
sin2 ✓0
2g
vi = ver ln
Mi
Mf
!(t) = !0 + ↵t
W =⌧ ✓
X
I=
mi ri2
i
~ = ~r ⇥ p~ = I~!
L
r2 dm
~
dL
dt
~⌧ = I~
↵
5
@U
k̂
@z
Isolid
mv î
2
= M R2
5
1
K = I! 2
2
Ihollow
sphere
K
mv 0 î + M u0 î
M uî =
sphere
u0
v0
GmM
r̂
r2
F~ =
T2 =
d2 x
dt2
d2 x
m 2
dt
m
U
4⇡ 2
a3
G(M1 + M2 )
v
d2 x
m 2 + kx = 0
dt
dx
+ b + kx = 0
dt
dx
+ b + kx = F0 cos(!drive t)
dt
F0
Adrive = p
2
2
2
m (!drive !02 )2 + b2 !drive
s
✓
◆2
k
b
!D =
m
2m
D(x, t) = A sin(kx
!t + )
v=f
F~ =
x(t) = A cos(!t + )
x(t) = Ae
1 q1 q2
r̂
4⇡✏0 r2
bt/2m
cos(!D t + )
x(t) = Adrive cos(!drive t + drive )
✓
◆
b !drive
1
drive = tan
2
m(!drive
!02 )
D(x, t) = A sin(
fr =
2⇡
x
2⇡f t + )
v ± vr
fs
v ⌥ vs
~
F~ = q E
Qq
4⇡✏0 r
~ = @V î @V ĵ
E
@x
@y
I
X
~ · dA
~= 1
E
qenc
✏0
✏A
C=
d
p~ = q d~
Vb
2
= M R2
3
1
1
= mv 2 + I! 2
2
2
2mv + (m M )u
=
M +m
2M u + (M m)v
=
M +m
GmM
=
s r ✓
◆
2 1
= GM
r a
U=
U = qV
Z b
~ · d~r
Va =
E
a
Q = CV
6
@V
k̂
@z
1
U = CV 2
2
N
X
Cparallel =
Ci
Rseries =
i=1
N
X
1
uE = ✏0 E 2
2
N
X
1
1
=
Cseries
Ci
i=1
1
Ri
Rparallel
i=1
V
R
P = I 2R
Z
~ ⇥ d~l
F~ = I B
=
N
X
1
Ri
i=1
l
A
~
F~ = q~v ⇥ B
qB
!=
m
~
~⌧ = µ
~ ⇥B
I
X
~ · d~l = µ0
B
Ienc
I=
R=⇢
~
µ
~ = IA
µ0 Id~l ⇥ r̂
4⇡ r2
F12
µ0 I 1 I 2
=
l
2⇡R
~ =
dB
µn =
e
~n
2m
Fundamental Constants
G = 6.673 ⇥ 10
11
m3 kg
1
s
2
NA = 6.022 ⇥ 1023 particles mol
✏0 = 8.854 ⇥ 10 12 C2 N 1 m 2
~ = 1.055 ⇥ 10 34 J · s
7
1
c = 2.997 ⇥ 108 m s
1
e = 1.602 ⇥ 10 19 C
µ0 = 4⇡ ⇥ 10 7 N A 2