We know the tidal waves are decreasing the spin rate of the earth which causes the days to longer, so as the angular momentum of the earth decreases it means it rotational kinetic energy also decreases since energy is always conserved the translational kinetic energy of earth must increase now right? Then that would cause number of days in a year to decrease as we right?
since energy is always conserved the translational kinetic energy of earth must increase now right?
Energy is conserved, but kinetic energy is not necessarily conserved. In this case, the tidal drag converts some of the kinetic energy of the earth-moon system into thermal energy.
It's very similar to simple friction in other contexts. If you slide a book across a table, it comes to a stop. Momentum (of the earth-book system) is conserved, but kinetic energy is not.
Then that would cause number of days in a year to decrease as we right?
Maybe you should read this article as a lot more goes into the kinematics of the earth around the sun,
Earth rotates faster than the moon orbits it, so the watery tidal bulge travels ahead of the moon's relative position. This displaced mass gravitationally tugs the moon forward, imparting energy and giving the satellite an orbital boost, whereas friction along the seafloor curbs Earth's rotation.
Hints of inconsistent Earthly timekeeping come through natural calendars preserved in fossils. Corals, for example, go through daily and seasonal growing cycles that form bands akin to growth rings in trees; counting them shows how many days passed in a year. In the early Carboniferous period some 350 million years ago an Earth year was around 385 days, ancient corals indicate, meaning not that it took longer for the planet to revolve around the sun, but that a day–night cycle was less than 23 hours long