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Can we put energy in to speed it up?

That way a day can be 24 hours exactly instead of 23 hours, 56 minutes, 4 seconds, etc...

Don’t follow your logic: if the day is currently shorter than 24 hours we need to slow the Earth rotation down, not speed it up.

You’re right, I had that backwards

I mean, solar day is 24h, it's the sidereal day that's 23.9344696h