So all the energy for movement comes from the lowering of the high of the paper ...
we must assume there is zero loss
At time 0 the paper is stationary with it's center of mass a height R above the table ...
At any moment after that the height (and mass) of the roll has been reduced and this is the energy which goes ..
1 ... into the rotation of the remaining roll (you need moment of inertia and angular speed)
2. ... into the forward velocity of the remaining roll (1/2 m v squared)
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Last edited by oz93666; Nov 8th 2018 at 01:21 AM.
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