Randall Munroe received a question from a 5-year-old and tackled it in excruciating detail on his site What If?
My son (5y) asked me today: If there were a kind of a fireman's pole from the Moon down to the Earth, how long would it take to slide all the way from the Moon to the Earth?
We can picture what the child was thinking, but to be quite accurate, Munroe first had to go through the reasons we can't install a fire pole between the earth and the moon. Then he discarded those reasons in order to answer the question about a fire pole that existed anyway. The first problem is that if you are standing on the moon, you have to go up the fire pole first.
If you climb up the pole far enough, Earth's gravity will take over and start pulling you down. When you're hanging onto the pole, there are three forces pulling on you: The Earth's gravity pulling you toward Earth, the Moon's gravity pulling you away from Earth, and centrifugal force from the swinging pole pulling you away from Earth. At first, the combination of the Moon's gravity and centrifugal force are stronger, pulling you toward the Moon, but as you get closer to the Earth, Earth's gravity takes over. The Earth is pretty big, so you reach this point—which is known as the L1 Lagrange point—while you're still pretty close to the Moon.
Unfortunately for you, space is big, so "pretty close" is still a long way. Even if you climb at better-than-world-record speed, it will still take you several years to get to the L1 crossover point.
But that's when the fun starts! As you let gravity take you down to earth, you have to deal with increasing speed, friction, weather, and the movement of the earth. I hope you brought your parachute. Munroe's highly-detailed answer probably won't be a lot of fun for a 5-year-old dreaming of space travel, but for we nerds who enjoy his xkcd comics, it's a pretty cool story. -via Metafilter