RIII-1 Phys2010 Exam 3 Review: Chapters 1 through 7 , 12 (see previous reviews) Chapter 8: Momentum • netdpFdt=KK ⇒ Impulse = netpF∆= ⋅∆tKK • Conservation of Momentum: netF0 pconstant=⇒=KK for system isolated from outside forces, tot 1 1 2 2p m v m v constant=+=KKK • Collisions: totpK always conserved. KE is conserved only in perfectly elastic collisions • 2D collisions: px,tot and py,tot are separately conserved. Chapter 9, 10: Rotations Analogy between rotation about a fixed axis and 1D translation along the x-axis: • sd(rads) = , = rdtθωθ= ω α,ddt ( like dx dvx v = , a = dt dt, ) • vtan = r ω , atan = r α • torque rF⊥τ= ⋅ • moment of inertia 2iiiImr=∑ • τnet = I ⋅ α ( like Fnet = m a ) • KErotation = (1/2) I ω2 [ like KEtrans = (1/2) m v2 ] • Rolling motion: KEtot = KEtrans + KErot = 221122mv Iω+ Angular Momentum • , rFτ≡ ×KKKL r p (for particle) L I for rotating object)≡× ⇒ =ωKKKK K(• net netdL dp(like F = )dt dtτ=KKKK • Conservation of Angular momentum: If netdL0 0 L constantdtτ= ⇒ = ⇒ =KKKRIII-2 L = constant ⇒ Ii ωi = If ωf Chapter 11: Static Equilibrium xyF0, F0==∑∑and 0τ=∑ The net torque about any axis must be zero. Chapter 13: Simple Harmonic Motion • Frestore ∝ −x , PE ∝ x2 , • period T independent of amplitude A, • sinusoidal motion Differential Equation: 2net2dx kFma kx makx,dt m==− ⇒ =− =−x Mass m on spring k, 2kTmπω= = ()2x(t) Acos tv(t) A sin( t )a(t) A cos( t )=ω+ϕ=− ω ω+ϕ=− ω ω+ϕ. Conservation of Energy: 22 2tot tot max11 1 1mv kx E E kA mv22 2 2+=⇒= =2Simple Pendulum: SHM in limit of small amplitude: gLω= Remember: to solve any before/after problem in an isolated system, try Conservation of energy or Conservation of momentum or Conservation of angular momentum. To prepare for Exams: • Review Concept Tests and CAPA problems. Read question and recall reasoning that gets to the answer. Be able to solve CAPA algebraically. • Prepare your formula sheet. • Take the practice exam. • It is no good to memorize answers. You have to understand and remember how you construct the