Problem 4 English Version

The body of a modified Yo-Yo consists of a pair of disks (radius R) rigidly connected by a central shaft (radius r).  The body has a total mass m.  Two pieces of string are used to wind this device as shown here.  The winding are such that a counterclockwise rotation in this figure, will unwind string from the shaft, and wind string up on the outer disks.  Each piece of string is wound in many layers (having zero thickness!) so that you are never concerned with comming to the ends of the string.  The slack section of string shown is looped over a frictionless pin located a distance yo directly above the center of the Yo-Yo.

After the system has been prepared, two experiments are performed.  In the first, the string is held in place on the supporting pin by placing a finger on top of the pin, and the device is released.  Then sufficient time is allowed for the re-establishment of equilibrium.

• If you believe that the equilibrium configuration is different from the initial configuration, determine what this difference is.  Otherwise state why you think the configuration does not change.

• Find the tension in each string in this equilibrium configuration.

In the second experiment, the device is returned to its original condition, and then simply released, with no clamping at the pin, so that the string may freely slip in either direction.

• Describe qualitatively the initial behavior of the system.  Provide a physical argument that supports any conclusions you draw concerning position, velocity, acceleration, and their rotational counterparts.

• Describe qualitatively the very long term behavior of the system.  Provide a physical argument that supports any conclusions you draw concerning position, velocity, acceleration, and their rotational counterparts.
 
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