For the same reason you strike with a point far away from the handle with just about every tool or weapon used to hit stuff (hammer, axe, baseball bat, sword), the end moves a lot faster than your hand, and hits harder. (although in this case we only really care about the speed)
If the rotation speed is constant, the tip of a longer object rotating around a fixed point will move faster than that of a shorter one. (Since the circle it has to traverse is longer.)
A combination of similar effects is why the tip of a whip can break the sound barrier even though your arm isn’t moving anywhere that fast.
To put it in slightly more physics-y terms, you move the end of whatever long thing you’re holding that’s close to your hand pretty slowly at a heavy mechanical disadvantage, and in exchange the far end moves really fast.
It’s kind of like pushing on the short arm of a lever, it’s hard but if you *can* move it, the other end will move very far quickly.
(and in reverse, it’s why it’s very hard to hold a stick steady if someone was free to push on the far end)
In addition to what other people have said already, follow through is significant.
Basically, we don’t really like to hurt ourselves, so if we’re trying to squash a bug against a hard surface, we’re going to try to slow our hand down to a safe speed right before hitting the surface, which is counter productive.
Swatting with an inanimate object, we aren’t worried about pain so we can maintain full speed through the whole swing.
This is something I learned in grade school, but it’s been awhile so my information may have been debunked in the last 30 years or so.
As I understand it, houseflies are covered in hairs that can detect sudden changes in the air caused by flat objects with lots of air resistance – like your hand – flying towards it.
Like make a fanning motion towards your face as though you were cooling yourself – feel that air moving on your face? A housefly is at least ten times more sensitive to that and moves out of the way before your hand even has time to get halfway there.
A fly swatter, on the other hand, has holes in it that allow air to pass right through it so that the fly never feels it coming. A blade or whip has something of the same effect – assuming your aim is good enough to bisect a fly.
On a more interesting note, carnivorous plants take a more methodical approach, moving ever so slightly when a fly lands on it as to not alert it, only moving quickly when there’s no room for the prey to maneuver.
Air acts like a fluid. So when we wave our hands quickly through the stuff, we create a thick layer of air in front of it. So even if the fly didn’t see your hand coming, it detects that air before your hands reaches it. Flies sure fast enough to get out of the way even with that little warning. Plus, they get to surf that layer, which acts like a pillow that softly pushes them away.
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