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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 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, http://www.phy.duke.edu/~hsg/

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 22

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 3 1 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 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 4 2 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 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 5 3 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 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 66 ANNOUNCEMENTS

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 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 2014-2015 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 2014-2015 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 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 10 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 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 11 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 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 12 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 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 13

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 14 IV6 Exit Homework Problem #1

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 15 IV6 Exit Homework Problem #2

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PHYS-1600/2000PHYS-1600/2000 IV6 Angular Energy and MomentumNEBRASKA WESLEYAN UNIVERSITYFALL 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 16 1 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 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 17 2 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 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 18 3 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 2014-2015 DEAN SIEGLAFF NATHANIEL CUNNINGHAM of 18 19 14141414 25252525 3333 PROJECTION SCREEN 6666 IV6: HAND IN TODAY’S ACTIVITIES SHEETS

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Physics 2211: Lecture 38 Rolling Motion

Physics 2211: Lecture 38 Rolling Motion

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