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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 1 Puzzler: A painter is high up on a ladder, painting a house, when unfortunately the ladder starts to fall over from the vertical. Determine which is less harmful for the painter: 1.to let go of the ladder right away and fall to the ground, or 2.to hang on to the ladder all the way to the ground. credit: Prof. Henry Greenside, Duke University,

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 22

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 A cylinder of wood and a hoop of iron, both of same radius and mass, are released from rest at the top of an inclined plane. Both roll without slipping. Which object reaches the bottom of the ramp first? 1.The cylinder 2.The hoop 3.They both will have arrived at the same time. 4.Need more information.

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 Two ice skaters each hold the end of a 6-m long rope as they skate, giving them a circular path of motion with an initial angular speed . As they skate they slowly and steadily pull upon the rope drawing themselves closer to one another until the diameter of their circular path is reduced to 3-m. Neglect friction between the skates and the ice. Their final speed will be 1.Equal to 0.5 2.Equal to 3.Equal to 2 4.Equal to 4 PATH OF MOTION v v

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 Two ice skaters each hold the end of a 6-m long rope as they skate, giving them a circular path of motion with an initial angular speed . As they skate they slowly and steadily pull upon the rope drawing themselves closer to one another until the diameter of their circular path is reduced to 3-m. Neglect friction between the skates and the ice. Their kinetic energy will have 1.Decreased to half the initial value. 2.Stayed the same. 3.Doubled. 4.Quadrupled. PATH OF MOTION v v

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of ANNOUNCEMENTS

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 7 Angular KE and the Work – Energy Theorem TRANSLATIONAL DYNAMICS (LINEAR DYNAMICS) ROTATIONAL DYNAMICS (ANGULAR DYNAMICS) All quantities have units of J.

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 8 Conservation of Mechanical Energy with Angular Motion Body rolling without slipping down an incline: mg FNFN F Fr a Is mechanical energy conserved? Yes No (circle one). Why?

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 9 Rolling Without Slipping Imagine a circular body rolling along a surface, experiencing static friction adequate to prevent slippage (relative motion) between the surface and the point of contact: v GROUND FRAME OF REFERENCE BODY FRAME OF REFERENCE v P a a

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of Conservation of Mechanical Energy with Angular Motion y “1”“1” “2”“2” h 0 v = 0 v

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of Conservation of Mechanical Energy with Rotational Motion PURE TRANSLATIONANGULAR INERTIA TERM

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of Angular Momentum TRANSLATIONAL DYNAMICSROTATIONAL DYNAMICS In the absence of external angular impulses: REMARKABLE PHYSICAL BEHAVIORS RESULT FOR BODIES WHOSE MOMENTS OF INERTIA ARE VARIABLE.

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 13

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of IV6 Exit Homework Problem #1

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of IV6 Exit Homework Problem #2

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 A cylinder of wood and a hoop of iron, both of same radius and mass, are released from rest at the top of an inclined plane. Both roll without slipping. Which object reaches the bottom of the ramp first? 1.The cylinder 2.The hoop 3.They both will have arrived at the same time. 4.Need more information.

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 Two ice skaters each hold the end of a 6-m long rope as they skate, giving them a circular path of motion with an initial angular speed . As they skate they slowly and steadily pull upon the rope drawing themselves closer to one another until the diameter of their circular path is reduced to 3-m. Neglect friction between the skates and the ice. Their final speed will be 1.Equal to 0.5 2.Equal to 3.Equal to 2 4.Equal to 4 PATH OF MOTION v v

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of of 3 Two ice skaters each hold the end of a 6-m long rope as they skate, giving them a circular path of motion with an initial angular speed . As they skate they slowly and steadily pull upon the rope drawing themselves closer to one another until the diameter of their circular path is reduced to 3-m. Neglect friction between the skates and the ice. Their kinetic energy will have 1.Decreased to half the initial value. 2.Stayed the same. 3.Doubled. 4.Quadrupled. PATH OF MOTION v v

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL DEAN SIEGLAFF NATHANIEL CUNNINGHAM of PROJECTION SCREEN 6666 IV6: HAND IN TODAY’S ACTIVITIES SHEETS

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