UNIT 10-18 FORMULA SHEET - UNIT 10 FORMULA SHEET...

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UNIT 10 FORMULA SHEET Gravitational formulae Electrostatic formulae Linear motion with constant acceleration a F = G m 1 m 2 r 2 F = m g , with g = G M r 2 F coul = k q 1 q 2 r 2 F = q E x = x i + v ix t + 1 2 a x t 2 v x = v ix + a x t v 2 x v ix 2 = 2 a x ( x x i ) Potential: – G M r Potential: V = U E q = k Q r F = m v 2 r Circular motion Potential energy: U g = G m 1 m 2 r ( U g = 0 at r = ) Δ U g = m g Δ h Potential energy: U E = k q 1 q 2 r ( U E = 0 at r = ) Δ U E = q Δ V T 2 = 4 π 2 R 3 GM (Planetary motion) E = k Q r 2 Electric field where k = 1 4 πε 0 and ε 0 = permittivity of free space E = – Δ V d Electric field for parallel plates τ = q d E sin θ Torque on an electric dipole E = Q 0 A = σ 0 where = Q A Electric field for parallel plate capacitor Φ E = E A = EA = EA cos Electric flux Φ E = 4 π kq = q/ ε 0 Gauss's law C = Q Δ V = κ ε o A d = A 4 kd Capacitance where = E o E Dielectric constant E = q κε 0 A = σ 0 Electric field for parallel plate capacitor with dielectric U = 1 2 Q Δ V = 1 2 C ( Δ V ) 2 = 1 2 Q 2 C Energy stored in a capacitor Energy density = Energy Volume = u = U Ad = 8 k E 2 = 1 2 0 E 2 Constants G 6.673 × 10 –11 N·m 2 ·kg –2 m e 9.109 × 10 –31 kg M Earth 5.975 × 10 24 kg e 1.602 × 10 –19 C R Earth 6.371 × 10 6 m k 8.99 × 10 9 N·m 2 ·C –2 R E orbital 1.50 × 10 11 m 0 8.85 × 10 –12 C 2 ·N –1 ·m –2
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UNIT 11 FORMULA SHEET Δ U E = q Δ V W = ε q V = Ir E = Δ V Δ s I = Δ q Δ t I = Δ Q Δ t = neA v D R = Δ V I R = ρ L A = 0 (1 + α Δ T ) P = I Δ V P = Δ U E Δ t Σ ε = Σ I R single loop P = I 2 R = V 2 R for resistor P = I I 2 r r is internal resistance of source C = Q Δ V C = 0 κ A d U = 1 2 C ( Δ V ) 2 = Q 2 2 C exponential e 2.72 V C ( t ) = 1 – e t/ τ charging a capacitor V C ( t ) = e t/ discharging a capacitor q (t) = q o 1 – e t/ charging a capacitor q (t) = q o e t/ discharging a capacitor I ( t ) = R e t/ charging or discharging a capacitor = RC time constant Kirchhoff's Rules Junction Rule: Σ I = 0 The sum of the magnitudes of the currents that flow into a junction equals the sum of the magnitudes of the currents that flow out of the same junction. Loop Rule: Σ Δ V = 0 Around any closed circuit loop, the algebraic sum of the potential drops equals the sum of the potential rises. Useful Constants e = 1.602 10 –19 coulombs 1 eV = 1.602 10 –19 joules 1 kcal = 4180 joules
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UNIT 12 FORMULA SHEET x = 1 2 at 2 W = F x x a r = ω 2 r = v 2 r ω = 2 π T f = 1 T v = at Δ U g = mg Δ h F r = m v 2 r r = m v qB v 2 = 2 ax K = 1 2 m v 2 = p 2 2 m p = m v E = Δ V d W = ε q P = W t = F v F = q E ε = IR F E = k q 1 q 2 r 2 I = Δ q Δ t R = ρ L A P = I Δ V P = Δ U E Δ t F B = q v × B = q v B sin θ F = I L × B = I L B sin F = μ o I 1 I 2 L 2 r ( L = length of wire, r = separation of wires) τ = NIAB sin = Fr sin θ torque Σ B || Δ A = o I
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This note was uploaded on 09/30/2011 for the course PHYS 1101 at Cornell University (Engineering School).

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UNIT 10-18 FORMULA SHEET - UNIT 10 FORMULA SHEET...

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