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eqn-sheet-5 - Equations and Constants for Quiz 5(b g = 9.8...

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Equations and Constants for Quiz 5 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 ) . (c) A + B = ( A x + B x ı + ( A y + B y ) ˆ j ; (d) A · B = AB cos θ A, B = A x B x + A y B y . (e) d A/dt = ( dA x /dt ı + ( dA y /dt ) ˆ j . 2. position: (a) r = x ˆ ı + y ˆ j ; (b) displacement: d = r 2 r 1 ; (c) distance: d = | r 2 r 1 | . 3. velocity: (a) v AV G = ( r 2 r 1 ) / ( t 2 t 1 ) v = dr/dt as t 2 t 1 ; (b) speed: v = | v | . 4. acceleration: (a) a AV G = ( v 2 v 1 ) / ( t 2 t 1 ) a = dv/dt as t 2 t 1 ; 5. 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 ) . 6. constant acceleration in 3D: (a) v = v 0 + at ; (b) r = r 0 + v 0 t + at 2 / 2 . 7. Free fall: (a) a = 0ˆ ı g ˆ j ; (b) g = 9 . 8 m/s 2 ; 8. Newton’s Laws (a) v = constant if F NET = 0 ; (b) ma = F NET ; (c) F ( 1 on 2 ) = F ( 2 on 1 ) . 9. Everyday forces (a) weight on Earth: W = mg ; (b) tension: always pulls, constant throughout string; (c) normal force: to surfaces (d) friction: k to surfaces, opposes motion i. f K = μ K N ; ii. 0 f S f MAX S = μ S N ; iii.
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