The Moon is revolving around the Earth and its centripetal acceleration is towards the Earth. Does it mean that the Moon is freely falling towards Earth? What is the cause of the Moon orbiting around Earth without falling towards it?
Answer
The Moon is freely falling toward Earth, like you say. But it is also moving "sideways" quite quickly, so that it "misses" Earth and passes to the side. And continues to freely fall, and again misses passing to the side. Doing this in a continuous manner is called orbiting (or flying).
To be a bit more technical, it is the angular momentum (and energy) of the Earth-Moon system that prevents a collision. The system "wants" to minimize its energy, which would be achieved by a collision, but angular momentum must be conserved. So the system does the best it can at constantly "trying" to collide, and orbits.
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