Download Formula/Data Sheets for Physics Final Exam, July 2007 | PHYS 1111 and more Exams Physics in PDF only on Docsity! Physics 1111 Final Exam 30 July 2007 Formula/Data Sheets (Nothing written on these sheets will be graded) Kinematics: Definitions Translational: ~v ≡ ~∆r ∆t ~v ≡ lim ∆t→0 ~∆r ∆t ~a ≡ ~∆v ∆t ~a ≡ lim ∆t→0 ~∆v ∆t Rotational: ω ≡ ∆θ ∆t ω ≡ lim ∆t→0 ∆θ ∆t α ≡ ∆ω ∆t α ≡ lim ∆t→0 ∆ω ∆t Kinematics: Constant Acceleration Motion (ti = 0) Translational (constant ~a): ~∆r = 1 2 (~vi +~vf)t ~∆r = ~vit + 1 2 ~at2 ~∆v = ~at v2fx = v 2 ix + 2ax(∆x) Rotational (constant α): ∆θ = 1 2 (ωi + ωf)t ∆θ = ωit + 1 2 αt2 ∆ω = αt ω2f = ω 2 i + 2α(∆θ) Kinematics: Linear/Angular Relations, Radial Acceleration s = θr vt = ωr at = αr T = 2πr vt = 2π ω ar = v2t r = ω2r Translational Dynamics Definitions Work: W ≡ Fd cos θ (constant force) Power: P ≡ W t = Fv cos θ Kinetic energy: K ≡ 1 2 mv2 = p2/2m Potential energy: Wc = −∆U Total mechanical energy: E ≡ K + U Linear momentum: ~p ≡ m~v Impulse: ~I ≡ ~F∆t Center of mass: M~rcm ≡ ∑ i mi~ri CM momentum: M~vcm = ∑ i ~pi = ~ptot Theorems/Laws Newton’s 1st Law: ~Fnet = 0 =⇒ ~v constant Newton’s 2nd Law: ∑ ~F = m~a Newton’s 3rd Law: ~F12 = −~F21 Work-Energy Theorems: Wtot = ∆K Wnc = ∆E (E constant if Wnc = 0) Impulse-Momentum Theorem: ~I = ∆~p Newton’s 2nd Law (system of particles): ∑ ~Fext = M~acm Linear Momentum Conservation: If ∑ ~Fext = 0, then ~ptot is constant Relative Motion If ~vAB denotes “velocity of A with respect to B”, then ~vAB +~vBC = ~vAC . Physics 1111 Final Exam 30 July 2007 Rotational Dynamics Definitions Rotational inertia: I ≡ ∑i mir2i Torque: τ ≡ rF sin θ Angular momentum: L ≡ rp sin θ (single particle) L = Iω (rigid object) Work: W = τθ (constant torque) Power: P = W t = τω Kinetic energy: Krot ≡ 12Iω2 = L2/2I Theorems/Laws/Applications Newton’s 2nd Law: ∑ τ = Iα Angular Momentum Conservation: If ∑ τext = 0, then L is constant Total kinetic energy: Ktot = Ktrans + Krot = 1 2 Mv2cm + 1 2 Icmω 2 Rolling without slipping: ∆x = (∆θ)r, v = ωr, a = αr Friction fs ≤ µsN fk = µkN Gravitation Approximation at Earth’s surface: F = mg U = mgh Newtonian gravity: F = −Gm1m2/r2 U = −Gm1m2/r Orbital speed: v = √ GM/r Kepler’s Third Law: T 2 = 4π2r3/GM Simple Harmonic Motion Definitions: f ≡ 1 T , ω ≡ 2πf Kinematics: x(t) = A cos ωt, v(t) = −ωA sin ωt, a(t) = −ω2A cos ωt Energy: E = 1 2 mω2A2 Spring motion: F = −kx, U = 1 2 kx2, ω = √ k/m Wave Motion Wave speed on string: v = √ FT /µ Periodic wave condition: v = λf Doppler effect: f ′ = f ( 1 ± uo/v 1 ∓ us/v ) Beat frequency: fbeat ≡ |f1 − f2|
