PHYS 1441 – Section 501 Lecture #14AnnouncementsConservation of Angular MomentumExample for Angular Momentum ConservationSimilarity Between Linear and Rotational MotionsWednesday, July 21, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu1PHYS 1441 – Section 501Lecture #14Wednesday, July 21, 2004Dr. Jaehoon Yu•Angular Momentum and Its Conservation•A table of angular and linear quantity comparisonsToday’s homework is #7, due 6pm next Wednesday, July 28!!Wednesday, July 21, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu2Announcements•Term2 exam results–Average: 63.8–Top score: 94–How did you do in term 1? •60.9•2nd quiz next Monday, Aug. 2 –Section 8.6 – whatever we cover till next Wednesday•Final term exam Wednesday, Aug. 11–Covers: Section 8.6 – wherever we cover by Aug. 4–Review on Aug. 11•We will go through the exam problems together and will have individual discussions on how you could improveWednesday, July 21, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu3Conservation of Angular MomentumRemember under what condition the linear momentum is conserved?Linear momentum is conserved when the net external force is 0.i fL L=ur urThree important conservation laws for isolated system that does not get affected by external forcesAngular momentum of the system before and after a certain change is the same.By the same token, the angular momentum of a system is constant in both magnitude and direction, if the resultant external torque acting on the system is 0. iLurconstp extWhat does this mean?Mechanical EnergyLinear MomentumAngular MomentumconstL dtpdF 0dtLd0fL=urconstant=i fp p=ur uri i f fK U K U+ = +Wednesday, July 21, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu4Example for Angular Momentum Conservation A star rotates with a period of 30days about an axis through its center. After the star undergoes a supernova explosion, the stellar core, which had a radius of 1.0x104km, collapses into a neutron start of radius 3.0km. Determine the period of rotation of the neutron star. T2What is your guess about the answer?The period will be significantly shorter, because its radius got smaller.fiLL Let’s make some assumptions:1. There is no torque acting on it2. The shape remains spherical3. Its mass remains constantThe angular speed of the star with the period T isUsing angular momentum conservationThusfffiIIfiIIifiTmrmr222fTf2iifTrr22days30100.10.324days6107.2s23.0Wednesday, July 21, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu5Similarity Between Linear and Rotational MotionsAll physical quantities in linear and rotational motions show striking similarity.QuantitiesLinear RotationalMass Mass Moment of InertiaLength of motion Distance Angle (Radian)SpeedAccelerationForce Force TorqueWork Work WorkPowerMomentumKinetic Energy Kinetic Rotational2I mr=rvtD=DtqwD=DvatD=DtwaD=DmaF IcosW Fd q=vFP P221mvK 221IKRLMW tq=vmp IL
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