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

[eurekameh]

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.

 

[gneill]

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.

 

[eurekameh]

Isn't the force also causing a moment about the center of mass? Shouldn't this contribute to the work done?

 

[gneill]

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?

 

[eurekameh]

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?

 

[gneill]

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.