Answer 1:
You don't feel it because (1) it's small,
and (2)
because the gravity holding you to the Earth is
about three hundred times as strong.
The Earth
has a circumference of roughly 40,000 kilometers,
which is traversed in a 24hour day. This means
that you are traveling at about 450 meters a
second relative to the center of the Earth. I
don't know how strong you are on algebra, but the
physics equation that describes the Earth's motion
is a=v^{2}/r, where a is the
acceleration toward the
center of the planet that keeps you rotating
around the Earth's surface instead of flying off
on a tangent, v is the velocity, and
r is the
radius of the earth, 6400 kilometers.
Doing the
calculations, we find that you're accelerating at
3.3 centimeters per second each second (that means
that each second you are moving 3.3 centimeters
per second faster. However, since the movement is
going in the opposite direction at midnight, it
equals out to zero over the whole of a day). You
would feel this, though just barley.
However,
the acceleration due to gravity is about three
hundred times this, so even sitting on the equator
(where the Earth's rotation is the fastest), it
would be drowned out by gravity. You're
probably wondering how you can be moving 450
meters per second (which is a little over a
thousand miles per hour) and not feel it. That's
because you don't feel motion  you feel changes
in the rate of your motion. If you're sitting in a
car going on a freeway, you don't notice any
difference than if the car were going five miles
per hour on a driveway. Likewise, you can't tell
if you're riding in an airplane how fast the
airplane is flying just by feel.
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