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Equations (2010) - 1 Formulas for 1st Midterm One...

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1 Formulas for 1 st Midterm One dimensional motion in x: x = x 0 + v 0 t + 1 2 at 2 (1) v = v 0 + at (2) v 2 = v 2 0 + 2 a ( x x 0 ) (3) Projectile Motion: x y x = x 0 + v 0 x t y = y 0 + v 0 y t 1 2 gt 2 v x = v 0 x v y = v 0 y gt v 2 x = v 2 0 x v 2 y = v 2 0 y 2 g ( y y 0 ) Forces: Σ vector F = mvectora (4) F s μ s N (5) F k = μ k N (6) Circular Motion: a c = v 2 R (7) Newtonian Gravity: F = GmM R 2 (8) G = 6 . 67 × 10 11 N × m 2 kg 2 (9) 1
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2 Formulas for 2 nd Midterm Work and Energy: W = F bardbl d (10) KE translation = 1 2 mv 2 (11) PE gravity = mgy (12) PE spring = 1 2 kx 2 (13) W = Δ KE (14) W nonconservative = Δ KE + Δ PE (15) Momentum: vector p = mvectorv (16) vector F external = Δ vector p/ Δ t (17) Rotation – Translation Correspondence: Translation Rotation x or s θ θ = s/r v ω ω = v/r a α α = a/r m I I = Σ mr 2 F τ τ = r F = rF p L L = Σ τ = (18) KE rotation = 1 2 2 (19) W rotation = τ Δ θ (20) τ = Δ L/ Δ t (21) Static Equilibrium: Σ F x = 0 (22) Σ F y = 0 (23) Σ τ = 0 (24) 2
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3 Formulas for the Final Fluids: P 1 + 1 2 ρv 2 1 + ρgy 1 = P 2 + 1 2 ρv 2 2 + ρgy 2 (25) V olumeRateofFlow parenleftbigg m 3
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