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312_Physics ProblemsTechnical Physics

312_Physics ProblemsTechnical Physics - 314*P10.75 Rotation...

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314 Rotation of a Rigid Object About a Fixed Axis *P10.75 (a) As the bicycle frame moves forward at speed v , the center of each wheel moves forward at the same speed and the wheels turn at angular speed ω = v R . The total kinetic energy of the bicycle is KK K =+ trans rot or Km mv I m m R v R + F H G I K J + F H G I K J F H G I K J 1 2 22 1 2 1 2 2 1 2 2 2 frame wheel wheel frame wheel wheel bg . This yields m v = + = 1 2 3 1 2 844 30820 335 612 2 2 frame wheel kg kg m s J b g b g .. . . . (b) As the block moves forward with speed v , the top of each trunk moves forward at the same speed and the center of each trunk moves forward at speed v 2 . The angular speed of each roller is = v R 2 . As in part (a), we have one object undergoing pure translation and two identical objects rolling without slipping. The total kinetic energy of the system of the stone
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