- #36

Steve4Physics

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With an energy-based approach here, work done by kinetic (sliding) friction is a combination of the heat generated, the change in linear KE, the change in rotational KE. This ‘3-way split’ makes it messy.

The problem can be solved quite easily using ##F=ma,\tau = I \alpha## and simple kinematics.

During the initial (slipping-and-rolling) phase:

a) the linear velocity, ##v##, decreases uniformly from ##v_0##;

b) the angular velocity, ##\omega##, increases uniformly from 0.

Rolling-without-slipping starts when these match, i.e. when ##v = \omega R##.

I’d recommend first finding the time (not the distance) taken till ##v = \omega R##. Then take it from there.