# And must be measured about the same origin the

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and𝐿must be measured about the same origin.The average torque is given byԦ𝜏 =Δ𝐿Δ𝑡This is the rotational analog of N2L in the formσԦ𝐹 =𝑑 Ԧ𝑝𝑑𝑡.For the rotation of a symmetricalobject about thesymmetry axis, the angular momentum andangular velocity are related by:𝐿 = I𝜔
49Can an object moving in a straight line have nonzero angularmomentum?Quick Quiz RB-8
50Can an object moving in a straight line have nonzero angularmomentum?Quick Quiz RB-8
51
Conservation of Angular Momentum52If the net external torque acting on asystem is zero, its angular momentum isconserved:A change inIfor an isolatedsymmetrical object rotating about itssymmetry axis implies a change inangular speed:Examples: Stellar explosions (neutronstars), figure skaters, divers, …).LLfi0(ifffiifiωIωILL
53For an object moving in a straight line with a constant velocity, isthe angular momentum conserved?a)Yes.b)No.Quick Quiz RB-9
54For an object moving in a straight line with a constant velocity, isthe angular momentum conserved?a)Yes.b)No.Quick Quiz RB-9
Rotations Block 3Q155An ice figure skater starts out spinning at 0.85 revolutions persecond with her arms outstretched.She wears lightly weightedbracelets to enhance the spin-up effect when she pulls her arms in.a)Calculate her final rotational speed if her moment of inertia is3.6 kg.m2with her arms outstretched and 1.1 kg.m2with herarms pulled close to her body.b)Determine the increase in her rotational kinetic energy.c)Where does this added energy come from?
56A disk with moment of inertiaI1rotates about a frictionless, verticalaxle with angular speed𝜔𝑖.A second disk, this one having moment ofinertiaI2about the same axle and initially not rotating, drops onto thefirst disk.Because of friction between the surfaces, the two eventuallyreach the same angular speed𝜔𝑓.a)Calculate𝜔𝑓.b)Calculate the ratio of the final to the initial rotational energy.Rotations Block 3Q2
57A merry-go-round is a common piece of playground equipment.A 3.0-m-diameter merry-go-round with a mass of 250 kg is spinning at 20rpm.John runs tangent to the merry-go-round at 50 m/s, in the samedirection that it is turning, and jumps onto the outer edge.John’s mass is30 kg.a)What is the merry-go-round’s angular velocity, in rpm, after Johnjumps on?You can treat the merry-go-round as a cylinder and Johnas a point particle.b)What happens to the angular velocity of the merry-go-round andJohn if John now starts walking towards the center?Rotations Block 3Q3
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Term
Summer
Professor
NoProfessor
Tags
Rigid Body, Rotation