211-Sp16-EqnSheet.pdf

211-Sp16-EqnSheet.pdf - PHYS 211 Equation Sheet ⃗ +...

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Unformatted text preview: PHYS 211 Equation Sheet ⃗ + ⃗⃗ = ( + )̂ + ( + )̂ = |⃗| = √⃗ ∙ ⃗ = √2 + 2 + 2 c = ab sin( ); direction: RHR for ⃗ = ⃗ × ⃗⃗ ⃗ = ( − )̂ + ( − )̂ + ( − )̂ Δ⃗ Δ⃗ ⃗ = ̂ + ̂ + ̂ ⃗ = ⃗ = Δ Δ d d⃗ d d d⃗ d ⃗ = = ̂ + ̂ ⃗ = = ̂ + ̂ 2 d d d d d d Δ⃗ = ∫ ⃗ 2 2 ⃗ 2 2 1 Δ⃗ = ∫ ⃗ = 2 = 2 ̂ + 2 ̂ 1 2 2 = , + 2 Δ 1 2 2 2 = , + 2 Δ ⃗ = ⃗ + ⃗Δ ⃗ = ⃗ + ⃗ Δ + ⃗(Δ) 2 2 2 = , + 2 Δ ⃗ = ⃗ + ⃗ ⃗ = ⃗ + ⃗ ⃗ = ⃗ + ⃗ 2 2 s = r a = r = = = t = = 2 = = 2 2 1 1 = + Δ 2 = 2 + 2Δ = = = = + Δ + (Δ)2 2 2 ⃗ = ⃗ (constant mass) ⃗12 = −⃗21 1 2 1 ⃗⃗ = − 2 ̂ fk = k n ⃗ = ⃗ ⃗;12 = − ⃗ = −Δs⃗ ̂ fs ≤ s n 2 2 2 ⃗ ⃗ ≡ ∫ ⃗ = Δ⃗ ⃗ = ⃗ ⃗− = ⃗ Δ ⃗; = 1 1 1 1 2 1 Ug = mgy = 2 = 2 = − = (Δ)2 2 2 2 ⃗ ≡ ∫ ⃗ ∙ ⃗ ⃗ = − ̂ − ̂ − ̂ = Δ ⃗ = =| | Δ Δ ⃗ = ∫ U ≡ – Wcons. f = ∙ ⃗ ⃗ ∙ ⃗⃗ = cos() = + + Wnc = Wext + Wdiss Eth = fk d = –Wdiss Emech;i + Wext = Emech;f + Eth 1 − 2 22 2 − 1 21 1D Elastic 1; = 1; + 2; 2; = 2; + Collisions 1 + 2 1 + 2 1 + 2 1 + 2 1; ∑ ⃗ ∫ ⃗ ⃗⃗ = ⃗ × ⃗ = ∑ 2 or ∫ 2 ⃗ = or ⃗ = ⃗ × ⃗ ⃗⃗ ∑ ∫ ⃗ = Fixed Axle: I = ICoM + Md2 ⃗⃗ = ⃗ = ⃗ ⃗⃗ 2 x(t) = Acos(t + 0) v(t) = –A sin(t + 0) a(t) = –A cos(t + 0) Emech = U + K =√ ≈√ 2 2 (, ) = sin ( ± + ) () = 0 −2 ( + 0 ) = () = 0 − 2 = = = √ = ≈√ PHYS 211 FNL Equation Sheet Moments of Inertia (for uniform density) about center of mass 1 1 = 2 = 2 12 2 Spheres: 1 2 2 = = ℎ 12 Constant acceleration due to gravity (Earth) gravitational constant radius of the earth mass of the Earth Prefix femtopiconanomicromillicentikilomegagiga- Letter f p n m c k M G Symbol g 2 = 2 5 2 ℎ = 2 3 Value 9.80 m/s2 6.67 × 10–11 N m2 / kg2 6.37 × 106 m 5.98 × 1024 kg 3.14159 Unit Conversions Unit Comparisons –10 1 Å = 10 m 1 N = 1 kg m / s2 1 inch = 2.54 cm 1J=1Nm 1 mile = 1609 m 1W=1J/s 1 m/s = 2.24 mph G RE Meaning 10–15 10–12 10–9 10–6 10–3 10–2 103 106 109 1 Hz = 1 s–1 = 60 rpm 1 rev = 2 rad = 360° 1 lb = 4.45 N 1 u = 1.66 × 10–27 kg b b 2 4ac 2a SOHCAHTOA A A C sin( ) cos( ) tan( ) A 2 2 2 A +B =C C B B B cos( ) sin( ) tan( ) B C A sin() sin() sin() Angle Sine Cosine Tangent = = deg rad 2 2 2 c a 30° 1/2 /6 a = b + c – 2 b c cos( ) √3/2 √3/3 2 2 2 45° 1 /4 b = a + c – 2 a c cos() √2/2 √2/2 60° 1/2 /3 c2 = a2 + b2 – 2 a b cos() √3/2 √3 b sin( ± ) = sin() cos() ± cos()sin() cos( ± ) = sin() sin() ∓ cos()cos() ′ () for constants a, c and n (()) = (()()) = ′ ()() + ()′() () = 0 ( ) = −1 ( ) = ((())) = ′ (())′ () If: a x2 + b x + c = 0, (cos()) = − sin() then x (sin()) = cos() ∫ = +1 +1 + (n ≠ –1) (tan()) = sec 2 () ...
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