It's actually driving north south that changes the rotation speed. Because your 'real' speed gets higher as you get closer to the equator, you 'steal' momentum from the earth as you get closer to the equator.
Its effectively the same principle as a figure skater pulling in their arms when spinning, to spin faster.
Reminds me of a glorious question from undergraduate physics:
Calculate the change in the length of the Earth's day if the UK were to switch to vehicles driving on the right-hand side of the road rather than the left..
It was indeed all about the roundabouts. I forget the details but I do know it took us quite a while to get there(!)
Those tutorials filled me with dread at the time, but with hindsight they were - how can I put this - a fairly formative experience.
Watching your tutor use paper and pencil - and estimation - to calculate something like that was actually quite inspiring. That was, once it stopped being terrifying.