For a wheel rolling without slipping, static friction is what stops it sliding and my notes also say it supplies the torque that spins it up. Two lines later the same notes say that friction does no work.
If it is exerting a torque and the wheel is spinning faster than before, energy has gone somewhere. Where is it coming from if not from the friction force?
Accepted Answer
Work is the force times the displacement of the point the force acts on, and for rolling without slipping the contact point is instantaneously at rest.
Zero displacement, so zero work, however large the force is.
The energy is coming from whatever is actually driving the wheel: gravity, if it is rolling down a slope, or the axle torque if there is an engine. Friction is not adding energy, it is moving it between the translational store and the rotational one.
Be careful with "friction does no work" as a slogan, because two different statements get collapsed into it.
It does no work at the contact point, and no net work on the wheel as a whole. It certainly does exert a torque about the centre of mass, and that torque changes the rotational kinetic energy. The translational part changes by the same amount in the opposite direction, so the sum is untouched.
The moment it slips, all of that stops applying. Then the contact point is moving, friction is kinetic rather than static, and the missing energy turns up as heat.
Nothing slides, so nothing is rubbed. That is the same reason a rolling wheel does not heat its contact patch the way a skidding one does.
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