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 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 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 = r/dt as t t 0 ; (b) speed: v = | ±v | . 6. acceleration: (a) ±a AV G =( ±v ±v 0 ) / ( t t 0 ) ±a = v/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) m±a = ± F NET ; (c) ± F ( 1on2 )= ± F ( 2on1 ) . 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 = K N ; ii. f S f MAX S = S N ; iii. K < S ; 12. Uniform circular motion (a) a C = v 2 /r ; (b) a C points to center of circle; (c) period: T = 2 r/v ; (d) circumference: C = 2 R ; 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) Keplers 3rd law: T 2 = 4 2 GM r 3 . 1...
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