Physics 111 General Physics I
Final Exam Formula Sheet
speedave = distance/ ∆t
Linear Motion (Constant a):
vave = ∆x / ∆t = (vi + vf) / 2
aave = ∆v / ∆t
v = vi + a t
vf2 – vi2 = 2 a ∆x
∆x = vave t = (vi + vf) t /2
∆x = vi t + ½ a t2
Fnet = ma
Rotational Motion (Constant α):
ωave = ∆θ / ∆t = (ωi + ωf) / 2
αave = ∆ω / ∆t
ω = ωi + α t
ωf2 – ωi2 = 2 α ∆θ
∆θ = ωave t = (ωi + ωf) t / 2
∆θ = ωi t + ½ α t2
τnet = I α
Uniform Circular Motion:
acp = v2 / R= ω 2 / R
Fcp = m v2 / R = m ω 2 / R
Projectile Motion:
x = x0 + v0,x t
y = y0 + v0,y t – ½ g t2
Forces:
Fnet = ma
f k = µk N
f s ≤ µs N
Fspring = – k ∆x
Fg = Gm1m2 / r2
G = 6.67 × 10-11 N·m2/kg2
g = 9.81 m/s2
Work, Energy and Power:
K = ½ mv2
Ug = mgh
Uspring = ½ k ∆x 2
Wnet = ∆K = Fparallel d = Fd cos θ
Wnon-conservative = ∆(K + U) = ∆ E
E= K + U = constant , if Wnon-conservative=0
P=W/t
Quadratic Formula:
x = – b ± √ (b2 – 4ac)
2a
Center of Mass:
rCoM = ( ∑mi ri ) / ( ∑ mi )
vCoM = ( ∑mi vi ) / ( ∑ mi ) = psystem / ( ∑ mi )
Momentum and Impulse:
p = mv
I = ∆p = Faverage t
Angular Momentum:
L=Iω
Iparticles= ∑mi ri2
τ = F r┴
τnet =∆L / ∆t = I α
If τextenal =0 , Lsystem = ∑ I ω =constant
If Fextenal =0, psystem = ∑mi vi =constant
(collisions)
Linear & Rotational Variables:
s = R ∆θ
v=Rω
atan = R α
constant speed rotation: T = 2 π R/v = 2π / ω
Sound and waves:
vsound in air = 340 m/s
I = Energy /(Area*t) = Power / Area
Intensity ~ Amplitude2
β = (10 dB) log (I / I0)
I0 = 10-12 W/m2
v = λf
f=1/T
vwave on string = √(F / µ), µ = m/L
Nth Harmonic wavelength on a string: NλN =2L
Nth Harmonic frequency on a string: fN =Nv/2L
Simple Harmonic Motion:
T = 2π √(m/k) (mass on a spring)
T = 2π √(L/g) (simple pendulum)
f=1/T
ω = 2 π f =2 π /T
E=½ k A 2
x=A cos(ωt); v= – A ω sin(ωt)
F= – kx;
a=F/m= – A ω2 cos(ωt)
K=½ m v 2 = ½ K A 2 sin2(ωt)
U=½ k x2 = ½ k A2 cos2(ωt)
vmax= A ω ;
amax= A ω2
Doppler Effect:
P=F/A
Fluids:
ρ=m/V
P = Patm + ρgh
Patm = 1.013 × 105 Pa
Fb = ρfluid V\sub g
A1v1 = A2v2
P + ½ρv2 + ρgy = constant
Thermodynamics:
∆L = α L0 ∆T
∆V = β V0 ∆T, for solid β =3 α
Q = C ∆T = m c (Tf –Ti)
1 cal = 4.186 J; 1Cal=1000 cal
Qconduction / t = k A (∆T/L)
Qradiation / t = e σ Α (T4 –T4 surrounding)
Heat needed for phase change Q = m L
Temperature Conversions:
T=TK = TC + 273.15
TC = (5/9) [TF – 32]
TF = (9/5) TC + 32
∆S= ∆Q/T
Heat Engine:
W = Q h – Qc
e = W / Qh= 1– Qc / Qh ≤ emax = 1– Tc / Th
Carnot’s Engine: Qc / Qh = Tc / Th
Refrigerator or Heat Pump:
W = Qh – Qc = Qh (1– Qc / Qh)
Ideal Heat pump: Qc / Qh = Tc / Th
COP = Qc / W or COP=Qh / W
Ideal Gas Law:
PV = NkT = nRT
R = 8.31 J / (mol·K)
k = 1.38 × 10–23 J/K
Uinternal = (3/2) NkT =(3/2) nRT
W=P ∆V
∆ Uinternal =Q – W