The string from a spool is being pulled with the geometry shown such that the spool...

 

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The string from a spool is being pulled with the geometry shown such that the spool rolls without slipping. The spool has mass m and radius of gyration k. The force has magnitude T. Consider only values of the angle theta in the range 0<0< n/2. T r. 1. As a function of problem parameters, determine the range of values for 0 such that a. The spool rolls to the right b. The spool rolls to the left c. The spool cannot roll without slipping. 2. Does the solution to Part I depend on the radius of gyration of the spool? Why does this make sense? 3. Show that the critical value for Part 1.c corresponds to the case where the line extending from the string passes through the contact point of the spool with the ground. The string from a spool is being pulled with the geometry shown such that the spool rolls without slipping. The spool has mass m and radius of gyration k. The force has magnitude T. Consider only values of the angle theta in the range 0<0< n/2. T r. 1. As a function of problem parameters, determine the range of values for 0 such that a. The spool rolls to the right b. The spool rolls to the left c. The spool cannot roll without slipping. 2. Does the solution to Part I depend on the radius of gyration of the spool? Why does this make sense? 3. Show that the critical value for Part 1.c corresponds to the case where the line extending from the string passes through the contact point of the spool with the ground.

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