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Unformatted text preview: xample: A sphere of radius r is released from height h in a roller coaster with loop of radius R . What is the minimum h to keep the sphere on the track? R B A h new term If no slipping and r << R : r v CM mg+N 2 CM v mg N m R At the point B: The minimum velocity is fixed by N = 0: R h g v CM 2 7 10 2 (1) gR v CM 2 (2) Combining Eq. 1 & 2: R h 7 . 2 min (Without rotation the factor is 2.5) 2 2 1 2 2 1 2 I mv R mg gh CM B A E E 2 5 1 2 2 1 2 CM CM mv mv R mg gh 2 5 2 mr I For sphere: 2 5 1 2 2 1 CM mv I Example: 1 m of cord is wound around a flywheel of radius, 0.25 m and ass, 2 kg which is concentrated in the rim. The cord is pulled with a force of 100 N and drives the wheel without slipping. What is the final angular velocity of the wheel when the cord is exhausted? What is the period? F=100 N m=1 kg I=mR 2 v=R The pulling of the cord implies a fixed amount of work done on this system. If we equate...
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- Fall '08