Kinematic Equations 1
Δx = (vi + v f )t 2
1
Δx = vit + at 2 2
€
v f 2 = vi 2 + 2aΔx € ω f 2 = ωi 2 + 2αΔθ €
v f = vi + at € ω f = ωi + αt €
v=
€
€
€
€
€
€
€
€
€
€
€
2 πR
T
€
Force and Momentum 

Fnet = ma Ff = µFn Fg = mg mv 2
Fnet =
r
Fs = −kx 

p = mv 
 
J = Δp = Favgt €
€ Torque and Angular Momentum 

τ net = Iα 
ΔL

τ net =
Δt
  
τ = R × F I = ∑ mi ri 2 €
I disk =
Oscillation Equations 2π
ω = 2 πf =
T
k
ω=
m
€
PEg = mgh PEe =
1
mR 2 2
€ x(t) = A cos ωt 1 2
kx 2
€
v=
dx
dt
a=
T = 2π
L
g
€
€
Wave Equations d2 − d1 = nλ λ ω
= T κ
v = fλ =
F
v = T µ
µ=
€
m
L
2π
κ=
λ
P
A
nv
2L
fn =
λn =
2L
n
fn =
nv
4L
v=
β
ρ
v = 331
€
€
A = 4 πR 2 4L
n
λn =
n = 1, 2, 3... n = 1, 3, 5... €
€
€
m
T
s 273K
Po = ωvρso €
y(x,t) = Asin(κx − wt) I=
€
dv
dt
€
€
€
Energy Equations 1
KE = mv 2 2
1
KErot = Iω 2 2
€
€
i
€
€
€
€
€
€
Rotational Kinematic Equations 1
Δθ = (ωi + ω f )t 2
1
Δθ = ωit + αt 2 2
Po 2
I=
2 ρv
⎛ I ⎞
β = 10dB log⎜ −12 ⎟ ⎝ 10 ⎠
€
⎛ f + f ⎞
fbeats = f1 − f2 pitch = ⎜ 1 2 ⎟ ⎝ 2 ⎠
€
Thermal Expansion Equations Deformation Equations T (K ) = T (o C) + 273 stress =
F
A
ΔL = αLo ΔT strain =
ΔL
L
F
ΔL
=Y
A
L
€
€
ΔV = βV oΔT €
€
β = 3α €
Calorimetry and Phase Change Equations €
Q = mcΔT Fe = k
Q = mLv E=
Fe
q
a=
qE
m
E=
Q
εo A
Circuits Equations €
€
Q = mL f €
Electrical Potential Energy Equations PEE =
V=
kq1q2
r
PEE
q
€ I=
| q1 || q2 |
r2
Q
t
ΔV = IR €
ΔV = −Ed €
€
∑ ΔV = 0 €
Req = ∑ R €
€
Constants g = 9.8 m/s2 ∑I = ∑I
1
1
= ∑ Req
R
in
€
P = IΔV = I 2 R =
Geometry Formulae and Trigonometric Relations €
sin A sin B sin C
=
=
a
b
c
€
out
Loop
€
c 2 = a 2 + b 2 − 2ab cosC sin(A ± B) = sin A cos B ± cos Asin B €
€
€
€
Electric Force and Field Equations €
€
€
€ €
ΔV 2
R
Calorimetry and Phase Change Data for Water cice = 2.11 kJ/kgK me = 9.11 x 10-­31 kg cwater =4.183 kJ/kgK mp = 1.67 x 10-­27 kg csteam = 2.080 kJ/kgK e = 1.602 x 10-­19 C ε o = 8.854x10
−12
Nm 2
k = 9x10
C2
9
C2
N ⋅ m2
Lf = 334.0 kJ/kg Lv = 2257 kJ/kg