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Physics Final Equation Sheet
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Physics 111 General Physics I Final Exam Formula Sheet speed ave = distance/ ∆t Linear Motion (Constant a) : Rotational Motion (Constant α) : v ave = ∆x / ∆t = (v i + v f ) / 2 ω ave = ∆θ / ∆t = (ω i + ω f ) / 2 a ave = ∆v / ∆t α ave = ∆ω / ∆t v = v i + a t ω = ω i + α t v f 2 – v i 2 = 2 a ∆x ω f 2 – ω i 2 = 2 α ∆θ ∆x = v ave t = (v i + v f ) t /2 ∆θ = ω ave t = (ω i + ω f ) t / 2 ∆x = v i t + ½ a t 2 ∆θ = ω i t + ½ α t 2 F net = ma τ net = I α Uniform Circular Motion : Projectile Motion : a cp = v 2 / R= ω 2 / R x = x 0 + v 0,x t F cp = m v 2 / R = m ω 2 / R y = y 0 + v 0,y t – ½ g t 2 Forces : Work, Energy and Power : F net = ma K = ½ mv 2 f k = μ k N U g = mgh f s ≤ μ s N U spring = ½ k ∆x 2 F spring = – k ∆x W net = ∆K = F parallel d = Fd cos θ F g = Gm 1 m 2 / r 2 W non-conservative = ∆(K + U) = ∆ E G = 6.67 × 10 -11 N·m 2 /kg 2 E= K + U = constant , if W non-conservative =0 g = 9.81 m/s 2 P = W / t Quadratic Formula : Center of Mass : x = – b ± √ (b 2 – 4ac) r CoM = ( ∑m i r i ) / ( ∑ m i ) 2a v CoM = ( ∑m i v i ) / ( ∑ m i ) = p system / ( ∑ m i ) Momentum and Impulse : Angular Momentum : p = mv L = I ω I = ∆p = F average t I particles = ∑m i r i 2 τ = F r ┴ If F extenal =0, p system = ∑m i v i =constant τ net =∆L / ∆t = I α (collisions) If τ extenal =0 , L system = ∑ I ω =constant Linear & Rotational Variables : s = R ∆θ v = R ω constant speed rotation: T = 2 π R/v = 2π / ω a tan = R α
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Physics Equations for Final
Transcript of Physics Final Equation Sheet
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Physics 111 General Physics I Final Exam Formula Sheet
speedave = distance/ t Linear Motion (Constant a): Rotational Motion (Constant ): vave = x / t = (vi + vf) / 2 ave = / t = (i + f) / 2 aave = v / t ave = / t v = vi + a t = i + t vf2 vi2 = 2 a x f2 i2 = 2 x = vave t = (vi + vf) t /2 = ave t = (i + f) t / 2 x = vi t + a t2 = i t + t2 Fnet = ma net = I Uniform Circular Motion: Projectile Motion: acp = v2 / R= 2 / R x = x0 + v0,x t Fcp = m v2 / R = m 2 / R y = y0 + v0,y t g t2 Forces: Work, Energy and Power: Fnet = ma K = mv2 fk = k N Ug = mgh fs s N Uspring = k x 2 Fspring = k x Wnet = K = Fparallel d = Fd cos Fg = Gm1m2 / r2 Wnon-conservative = (K + U) = E G = 6.67 10-11 Nm2/kg2 E= K + U = constant , if Wnon-conservative=0 g = 9.81 m/s2 P = W / t Quadratic Formula: Center of Mass: x = b (b2 4ac) rCoM = ( mi ri ) / ( mi ) 2a vCoM = ( mi vi ) / ( mi ) = psystem / ( mi ) Momentum and Impulse: Angular Momentum: p = mv L = I I = p = Faverage t Iparticles= mi ri2 = F r If Fextenal =0, psystem = mi vi =constant net =L / t = I (collisions) If extenal =0 , Lsystem = I =constant Linear & Rotational Variables: s = R v = R constant speed rotation: T = 2 R/v = 2 / atan = R
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Sound and waves: Simple Harmonic Motion: vsound in air = 340 m/s T = 2 (m/k) (mass on a spring) I = Energy /(Area*t) = Power / Area T = 2 (L/g) (simple pendulum) Intensity ~ Amplitude2 f = 1 / T = (10 dB) log (I / I0) = 2 f =2 /T I0 = 10-12 W/m2 E= k A 2 v = f x=A cos(t); v= A sin(t) f = 1 / T F= kx; a=F/m= A 2 cos(t) vwave on string = (F / ), = m/L K= m v 2 = K A 2 sin2(t) Nth Harmonic wavelength on a string: NN =2L U= k x2 = k A2 cos2(t) Nth Harmonic frequency on a string: fN =Nv/2L vmax= A ; amax= A 2 Doppler Effect: P = F / A Thermodynamics: Fluids: L = L0 T = m / V V = V0 T, for solid =3 P = Patm + gh Q = C T = m c (Tf Ti) Patm = 1.013 105 Pa 1 cal = 4.186 J; 1Cal=1000 cal Fb = fluid V\sub g Qconduction / t = k A (T/L) A1v1 = A2v2 Qradiation / t = e (T4 T4 surrounding) P + v2 + gy = constant Heat needed for phase change Q = m L Temperature Conversions: S= Q/T T=TK = TC + 273.15 Heat Engine: TC = (5/9) [TF 32] W = Qh Qc TF = (9/5) TC + 32 e = W / Qh= 1 Qc / Qh emax = 1 Tc / Th Carnots Engine: Qc / Qh = Tc / Th Refrigerator or Heat Pump: W = Qh Qc = Qh (1 Qc / Qh) Ideal Heat pump: Qc / Qh = Tc / Th Ideal Gas Law: COP = Qc / W or COP=Qh / W PV = NkT = nRT R = 8.31 J / (molK) k = 1.38 1023 J/K Uinternal = (3/2) NkT =(3/2) nRT Uinternal =Q W W=P V
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