Work-Energy: Force Acting Through 1.2pi Despite 0.6pi Move

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The discussion centers on the relationship between force, distance, and energy in a system involving a disk and an unwinding cord. It highlights confusion regarding why the force acts through a distance of 1.2pi while the disk's center only moves 0.6pi. The unwinding cord increases in length, necessitating that the force's application point moves further than the disk itself. Additionally, the force generates a moment about the center of mass, which should contribute to the total kinetic energy of the disk, encompassing both translational and rotational components. The conversation concludes by affirming that the solution to the problem addresses both forms of kinetic energy.
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I don't understand why the force is acting through a distance of 1.2pi, even though the center of the disk clearly moves a distance of 0.6pi.
 
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The cord is unwinding. So the length of cord between where it meets the disk and whatever it is that's pulling on the cord will grow longer. Clearly whatever is applying the force to the free end of the cord has to mover further than the disk's center.
 
Isn't the force also causing a moment about the center of mass? Shouldn't this contribute to the work done?
 
eurekameh said:
Isn't the force also causing a moment about the center of mass? Shouldn't this contribute to the work done?

Doing work results in a change in energy, in this case a change in the energy of motion. Can you identify where the energy of motion is going to end up in this case?
 
Translational and rotational kinetic energy. The force moves through a distance of 1.2pi. But it is also causing a moment through an angle of 2pi. Shouldn't this moment through an angle also be contributing to the total kinetic energy (translational and rotational) of the disk?
 
eurekameh said:
Translational and rotational kinetic energy. The force moves through a distance of 1.2pi. But it is also causing a moment through an angle of 2pi. Shouldn't this moment through an angle also be contributing to the total kinetic energy (translational and rotational) of the disk?

You've identified translational and rotational kinetic energies to be where the work energy ends up. That's good. The solution included with the question deals with both.
 
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