Physics’1210’ Spring2016’ Prof.’Jang2Condell ...
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Physics 1210 Spring 2016 Prof. JangCondell Equation Sheet For Exam #3 v avg = x 2 − x 1 t 2 − t 1 = Δ x Δ t a avg = v 2 − v 1 t 2 − t 1 = Δ v Δ t a rad = v 2 R = 4π 2 R T 2 x 1 = x 0 + v 0 t + 1 2 at 2 v 1 = v 0 + at v 1 2 = v 0 2 + 2 a( x 1 − x 0 ) v = d r dt a = d v dt F ∑ = m a w = m g f s ≤ μ s N f k = μ k N f = kv f = Dv 2 f spring = −kx Work/Energy W = F ⋅ s = Fs cosθ W = ΔK K = 1 2 mv 2 U spring = 1 2 kx 2 U grav = mgy P = ΔW Δ t = F ⋅ v F = − dU dx Momentum/Impulse p = m v K 1 + U 1 + W other = K 2 + U 2 J = Δ( mv) = F Δt x cm = m i ∑ x i m ∑ i Angular Motion Kinematics power = τω θ 1 = θ 0 + ω 0 t + 1 2 α t 2 ω 1 = ω 0 + α t ω 2 1 = ω 0 2 + 2α ( θ 1 − θ 0 ) τ ∑ = I α I = m i r i 2 i ∑ I = I cm + Md 2 τ = r × F = rF sin φ ω = d θ dt α = dω dt s = r θ v = r ω a tan = r α a rad = ω 2 r W = ΔK = τ Δθ K rot = 1 2 Iω 2 K tot = 1 2 mv cm 2 + 1 2 I cm ω 2 L = r × p = rmv = Iω ΔL = τ Δt 2π = 360 g = 9.80 m/s 2
Transcript of Physics’1210’ Spring2016’ Prof.’Jang2Condell ...
Physics 1210 Spring 2016
Prof. Jang-‐Condell
Equation Sheet For Exam #3
vavg =x2 − x1t2 − t1
=ΔxΔ t
aavg =v2 − v1t2 − t1
=ΔvΔ t
arad =v2
R=4π 2RT 2x1 = x0 + v0t + 1
2 at2 v1 = v0 + at v1
2 = v02 + 2a(x1 − x0 )
v = drdt
a = dvdt
F∑ =ma
w =m g fs ≤ µsN fk = µkN f = k v f = Dv2 fspring = −kx
Work/Energy W =
F ⋅ s = Fscosθ
W = ΔK K = 12mv
2 Uspring = 12 kx
2 Ugrav =mgy
P = ΔWΔ t
=F ⋅ v
F = − dUdx
Momentum/Impulse p =mv
K1 +U1 +Wother = K2 +U2
J = Δ(mv) = FΔt xcm =mi∑ xim∑ i
Angular Motion
Kinematics
power = τω
θ1 =θ0 +ω 0 t + 12α t
2 ω1 =ω 0+α t ω 21 =ω0
2 + 2α (θ1 −θ0 )
τ∑ = IαI = miri
2
i∑ I = Icm +Md
2 τ =r ×F = rF sinφ
ω =dθdt
α =dωdt s = rθ v = rω atan = rα arad =ω
2r
W = ΔK = τ Δθ
Krot = 12 Iω
2 K tot = 12mvcm
2 + 12 Icmω
2L = r × p = rmv = Iω ΔL = τ Δt
2π = 360
g = 9.80 m/s2
Gravity G=6.67×10-11 N m2/kg2
Ug =−GM1M2
rFg =
GM1M2
r2v = Gm1
rT = 2πr
v= 2π r3
Gm1
Fluids p = dF⊥dA
p2 − p1 = −ρg(y2 − y1) p1 + ρgy1 + 12 ρv1
2 = p2 + ρgy2 + 12 ρv2
2
ρ1A1v1 = ρ2A2v2
Periodic Motion f =1 T ω = 2π f
ω =km ω =
gL
ω =mgdI
E = 12mv
2 + 12 kx
2 = 12 kA
2x = Acos(ωt +φ)
x = Ae−(b/2m)t cos( "ω t +φ); "ω =km−b2
4m2
Simple pendulum
Physical pendulum Damped oscillations
Mechanical Waves v = λ f y(x, t) = Acos(kx −ωt) k = 2πλ
v = ωk
v = Fµ f1 =
v2L fn = nf1, (n =1,2,3,…) Pav = 1
2 µFω 2A2
I = P4πr2
I1I2=r22
r12
Waves on a string
Sound
pmax = BkA
v = B ρI = pmax
2
2ρv=
pmax2
2 ρBβ = (10 dB)log I
I0
fn =nv4L, (n =1,3, 5,…)fn =
nv2L, (n =1,2,3,…) fbeat = fa − fb fL =
v+ vLv+ vS
fSOpen pipe Closed pipe
Spring
vesc =2Gm1r
