Study guide for final_fall2011

Study guide for final_fall2011 - Possibly useful equations:...

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1 Possibly useful equations: Chapter 1 Introduction Chapter 2 Vectors and motion along a line o Displacement (change in position): f i rr r Δ =− r rr . o Average velocity: av r v t Δ = Δ r r o Average acceleration: av v a t Δ = Δ r r o Constant acceleration equations: x fx ix x vvv a t Δ =−= () 1 2 f i fx ix x xx vv t Δ= − = + Δ 2 1 2 ix x x vt a t Δ + Δ 22 2 fx is x a x −= Δ o 2 9.80 m s g = ( always down!) Chapter 3 Two-dimensional motion sin opposite hypotenuse = cos adjacent hypotenuse = tan opposite adjacent = Chapter 4 Force and Newton’s Laws of Motion o Newton’s 2 nd Law: F a m = r r or Fm a = r r o The magnitude of the gravitational force: 12 2 Gm m F r = o Weight : Wm g = . o Static friction : ss f N μ o Kinetic friction : kk f N = Chapter 5 Circular Motion o Angular displacement: f i θ θθ Δ ; average angular velocity av t ω Δ = Δ r r o sr = , 1 complete circle = 1 revolution = 2 π radians o To relate linear to angular quantities: t vr = t ar α = o Acceleration in uniform circular motion: 2 2 r v r == o 2 v am r r r
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2 o fi t ω ωωα Δ= − = ; ( ) 1 2 f i t θθ θ ω ω + Δ ; () 2 1 2 i tt θω α Δ ; 22 2 ωα θ −= Δ o 1 f T = Chapter 6 Work and Energy o Work : cos WF r (If F and r are along the x -axis then x WFx ). o Translational kinetic energy : 2 1 2 trans Km v = . o The Work-Kinetic Energy Theorem : total WK = Δ o The gravitational potential energy : grav Um g y = o The potential energy associated with a spring : 2 1 2 spring Uk x = . o The force required to pull on a spring: spring Fk x = − o Conservation of energy : initial final E E = . Chapter 7 Momentum, Impulse and Conservation of Momentum o Linear momentum : p mv = rr ( Vector). o p Ft Δ= Δ r r . Chapter 8 Rotations, torques, and angular momentum o The rotational kinetic energy: 2 1 2 rot KI = o Rotational inertia: 2 I mr = o Torque: rF r F τ =× = ± r r o Angular momentum: L I = o Conservation of angular momentum : if 0, if LL = = Chapter 10 Simple Harmonic Motion (SHM) o The maximum velocity and acceleration in SHM: m vA = 2 m aA = o The equations of motion for SHM: If x = A at t = 0 If x = 0 at t = 0 cos sin cos xm x At vv t aa t = =− sin cos sin x t t = =
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3 o The mechanical energy for SHM: 22 2 111 222 mech SHM Ek A m v k x ==+ o The angular frequency for a mass-spring system: spring k m ω = o The angular frequency for a simple pendulum: pendulum g L = Chapter 11 Waves o Wave intensity (for an isotropic source): 2 4 power area P I r π == o The speed of transverse wave on a string: string F m v L μ o Harmonic traveling wave: ( ) ( ) ,c o s y xt A t kx =− o f, ω , λ are related! 2 f = ; f k v λ ; f v = o The speed of a wave : vf k = = o Standing wave on a string: the distance between two adjacent nodes is ½ λ . Chapter 12 Sound o Sound intensity level: () 2 12 0 0 10 dB log ; 1.00 10 W m I I I β ⎛⎞ × ⎜⎟ ⎝⎠ o Standing sound wave in a pipe open at both ends : 2 ; (n=1,2,3,. ..) 2 nn Lv fn nL o Standing sound wave in a pipe closed at one end : 4 ; (n=1,3,5,. ..) 4 o Doppler shift: 1 1 o os s v v f f v v = Chapter 13 Temperature and the ideal gas o Temperature scales and conversions : 273.15 C TT ; (1.8 / ) 32 FC TF C T F =+
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Study guide for final_fall2011 - Possibly useful equations:...

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