Study guide for final_fall2011

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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 = =
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 =+

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 14

Study guide for final_fall2011 - Possibly useful equations...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online