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eqn-sheet-2 - string(c normal force ⊥ to surfaces(d...

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Equations and Constants for Quiz 2 Note: you may detach this sheet from the quiz. You do not need to hand it in. 1. vectors: (a) A = ¯ ¯ ¯ A ¯ ¯ ¯ = q A 2 x + A 2 y ; (b) θ A = tan 1 ( A y /A x ) . 2. vector operations: (a) A + B = ( A x + B x ı + ( A y + B y ) ˆ j ; (b) A · B = AB cos θ A, B = A x B x + A y B y . 3. vector derivatives: d A/dt = ( dA x /dt ı + ( dA y /dt ) ˆ j . 4. position: (a) r = x ˆ ı + y ˆ j ; (b) displacement: d = r 2 r 1 ; (c) distance: d = | r 2 r 1 | . 5. velocity: (a) v AV G = ( r r 0 ) / ( t t 0 ) v = dr/dt as t t 0 ; (b) speed: v = | v | . 6. acceleration: (a) a AV G = ( v v 0 ) / ( t t 0 ) a = dv/dt as t t 0 ; 7. constant acceleration in 1D: (a) v = v 0 + at ; (b) x = x 0 + v 0 t + at 2 / 2 ; (c) v 2 = v 2 0 + 2 a ( x x 0 ) . 8. constant acceleration in 2D: (a) v = v 0 + at ; (b) r = r 0 + v 0 t + at 2 / 2 . 9. Free fall: (a) a = 0ˆ ı g ˆ j ; (b) g = 9 . 8 m/s 2 ; 10. Newton’s Laws (a) v = constant if F NET = 0 ; (b) ma = F NET ; (c) F ( 1 on 2 ) = F ( 2 on 1 ) . 11. Everyday forces (a) weight on earth: W = mg ; (b) tension: always pulls, constant throughout
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Unformatted text preview: string; (c) normal force: ⊥ to surfaces (d) friction: k to surfaces, opposes sliding i. f K = μ K N ; ii. ≤ f S ≤ f MAX S = μ S N ; iii. ≤ μ K < μ S ; 12. Uniform circular motion (a) a C = v 2 /r ; (b) ±a C points to center of circle; (c) period: T = 2 πr/v ; (d) circumference: C = 2 πR ; 13. Universal gravitation (a) ¯ ¯ ¯ ± F ¯ ¯ ¯ = Gm 1 m 2 r 2 12 ; (b) ± F ( 1 on 2 ) points from 2 to 1; (c) G = 6 . 7 × 10 − 11 N · kg − 2 · m 2 ; (d) Kepler’s 3rd law: T 2 = 4 π 2 GM r 3 . 1...
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