Why does the earth never slow down or stop turning?

Answer 1

Short answer: conservation of angular momentum.

Longer answer: there is very little friction to slow down the spinning. The planets are in the vacuum of outer space in orbit around the sun (you can think of an orbit as always falling at the sun, but always missing) and there are very few forces to oppose the spin of the planets.

There are some opposing forces though. Outer space is not a perfect vacuum, and so the earth does encounter a small amount of resistance as it orbits and spins. The earth is also pushed away from the sun by the force of sunlight (photons have momentum; they transfer it to the earth when they bounce off or are absorbed; then there's the solar wind). The spin of planets on their own axes is resisted very slightly by forces of tide.

So for example Mercury (closest to the sun, therefore highest tidal forces) spins only once on its axis for each orbit about the sun. Mercury thus always keeps the same face to the sun. It used to have more spin, but the greater tidal forces on Mercury have already reduced its spin to the stable configuration.

Likewise the Moon spins once per orbit. The moon exerts tidal forces on the Earth, and the Earth, being much more massive, exerts larger tidal forces on the Moon. The result is that the Moon now always keeps the same face towards the Earth (the stable configuration).

Just as the Moon lost its spin to Earth tidal forces, the Earth is slowly losing spin to solar tidal forces, so days are slowly getting longer (on the order of 1 or 2 milliseconds per century).

So the long answer is that the earth only seems to keep spinning because you have been observing it for such a short time. If you wait a billion or so years you'll notice it is slowing down!