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PHYS 170; GENERAL PHYSICS I Fall 2010; Prof. Szarmes WEEKLY PROBLEM SET 7 Due at start of class Monday, October 25, 2010 1. Rotating Cylinder I. A...
1. Rotating Cylinder I. A massless string is wrapped around the axle of a uniform, solid cylinder of mass m, radius r, and moment ICM = 1/2 mr2 about the center of mass. The axle is massless and has radius r/3. A tension force F < mg is applied to the string, causing the cylinder to roll without slipping as shown in the figure below. Note that in going from (a) to (c) the friction force f reverses direction.i) In figure (a), calculate the magnitude of the friction force f as a fraction of the pulling force F.ii) In figure (c), calculate the magnitude of the friction force f as a fraction of the pulling force F.iii) In figure (b), at what angle θ does the friction force equal zero?2. Rotating Cylinder II. Now, let’s continue to pull on the cylinder as shown in the figure below. Note that in going from (a) to (c) the acceleration of the center of mass (CM) reverses direction.i) In figure (a), calculate the acceleration of the CM as a fraction of F/m.ii) In figure (c), calculate the acceleration of the CM as a fraction of F/m.iii) In figure (b), at what angle θ does the acceleration of the CM equal zero?
