Unformatted text preview: Some Equations for the Final Exam • sin π 6 = sin30 ◦ = 1 2 ; sin π 2 = sin90 ◦ = 1; sin 5 π 6 = 1 2 ; sin 3 π 2 = 1 cos π 6 = cos30 ◦ = √ 3 2 ; cos π 2 = cos90 ◦ = 0; cos 5 π 6 = √ 3 2 ; cos 3 π 2 = 0 d dt sin( at + b ) = a cos( at + b ); d dt cos( at + b ) = a sin( at + b ) • Pressure vs depth h in a fluid of density ρ : p = p + ρgh , if p is pressure at the surface. • Archimedes’ Principle: The magnitude of the buoyant force on an object equals the weight of the fluid it displaces. • Equation of Continuity: ρAv = constant. • Bernoulli’s Equation: p + 1 2 ρv 2 + ρgh = constant. • If F = kx , U ( x ) = 1 2 kx 2 , and E = K + U = 1 2 kx 2 m , where x m is the amplitude. • For various simple harmonic oscillators, the period T is given by: Mass and spring : T = 2 π m k Simple pendulum : T = 2 π L g Torsional pendulum : T = 2 π I κ Physical pendulum : T = 2 π I mgd Recall, frequency f = 1 /T , and angular frequency ω = 2 πf = 2 π/T ....
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This note was uploaded on 04/30/2008 for the course PHY 317k taught by Professor Kopp during the Fall '07 term at University of Texas.
 Fall '07
 KOPP

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