1Phy 2053 Announcements1. Exam 2 on Thursday, 8:20 – 10:10 pm 20 questions, multiple choice  There is only one correct answer to the question “In order to receive credit for this problem, you must correctly code (“bubble in”) your UFID and your 5-digit test number…”Æ I have correctly bubbled my UFID number and 5-digit test code. Please get there at least 10 minutes early, and preferably 20 minutes New protocols - stay in your seat until your exam is collected. Raise your hands; proctors will come to collect it.  If you want to avoid the long wait at the end, either (a) come early and sit at the front or (b) finish early Please circle your answer on the exam More Phy 2053 Announcements Room assignments for Exam 2 BRY130: A-ELU FLG220: EMM-HER FLG230: HEW-LAI FLG260: LAM-MON  FLG270: MOO-P LIT121: R-SAW MAEB211:SCH-T MAT18: U-Z You be allowed one handwritten formula sheet (both sides), 8 ½” x 11” paperReview – Exam 2 Exam 2 will cover from Chapter 5.4 through Chapter 8 No testing of material that was not covered in class  Eg, Kepler’s Laws Concepts and material that you have learned from the beginning of the course will be needed Physics builds on itself!Important concepts from the beginning of the course 1D Kinematics Newton’s Laws: Σ F = ma Equilibrium, free-body diagrams, relationship between friction and normal force Work: (Translational) Kinetic Energy: Work-energy theorem: Potential energy Gravitational potential energy: PEg= mgy Conservation of mechanical energy x)cosF(W Δθ≡2)2/1( mvKEt=Chapter 5 Springs Hooke’s Law: F = - k x Spring potential energy: Power P = Work/time = FΔx/ t Average Power P = F v221kxPEs=Chapter 6  Linear momentum p = mv Relationship between force and momentum: F = Δ p/Δ t Impulse: When force is not constant, use average force  Conservation of momentum Always conserved, but conservation most useful in isolated systems involving collisions (no external forces) the total momentum before the collision will equal the total momentum after the collisiontFpI Δ=Δ=rrr2Chapter 6  Types of collisions Head-on, 1D collisions Inelastic collisions Mechanical energy is not conserved in the collision Perfectly inelastic collisions occur when the objects stick together after the collision  Final velocity vfis the same for both objects Example is the famous ballistic pendulum  Elastic collision both momentum and kinetic energy are conserved For one dimensional head-on collisions: v1i+ v1f= v2i+ v2f 2D collisions (and glancing collisions): x-direction:  y-direction:xxxxyyyyNo questions onRocket propulsionChapter 7  Rotational kinematics: Angle θ, angular velocity ω, angular acceleration αω = Δθ/Δt, α = Δω/Δt relationship between angular and linear quantities Displacement: Velocity: Acceleration:rsθΔ=Δtvrω=tarα=Chapter 7  Centripetal acceleration magnitude given by Relationship to angular velocity:  Centripetal force force that keeps an object following a circular pathFC= maC Eg, tension in a string, gravity, friction Banked curves: Loop-the-loop: Total acceleration:raC2ω=2cvar=tgRvtop=2C2taaa +=Chapter 7  Newton’s universal law of gravitation Acceleration due to gravity varies with distance from the center of the earth General expression for gravitational potential energy221rmmGF =2ErMGg =rmMGPEE−=No questions onescape velocity Chapter 8 Torque, τ = r F ^ Torque and equilibrium First condition: Second condition: Solving rotational equilibrium problems: Pick coordinate system and draw free-body diagram Apply Pick axis to sum torques and apply 000xyorandΣ=Σ= Σ=FFFrrrτ = r F sin θ0τΣ=r0τΣ=rChapter 8 Torque and angular acceleration: Moment of inertia I: Table 8-1 lists moments of inertia for different objects Rotational dynamics – Newton’s 2ndLaw for rotation Bucket problem Rotational kinetic energy: Mechanical conservation laws still apply!  Angular momentum:  Conservation of angular momentum (isolated system): The angular momentum of a system is conserved when the net external torque acting on the systems is zero.IταΣ=22iiImrMR=Σ =ω=21KE2IL = I ω0,if iiffLLorI IτωωΣ= = =3Newton’s Second Law for Rotation--Example Draw free body diagrams of each object Only the cylinder is rotating,so apply Στ = I α The bucket is falling, but not rotating, so apply ΣF = ma Remember a = α r andsolve the resulting