Answer 1:
What a great question!
We have a rotating space station shaped like a
wheel with some radius r, rotating with a constant
angular velocity ω = R, and two astronauts. We'll
say the astronauts, named Fred and Jorge, have the
same mass. Fred is standing at some computer
terminal, and Jorge is running laps so he can look
trim for all the handsome people on Earth. Neither
of them is accelerating.
Let's talk Newton's laws. His second law states
that the sum of the forces acting on any object
is equal to the mass of that object times its
acceleration (F = m*a). Acceleration is the
change in velocity with respect to time.
Before we go any further, let's define our
directions, or coordinates. Let's say the
astronauts can move in two directions, either
towards or away from the center of the space
station or tangent to the circular space station.
Tangent means perpendicular to the line connecting
the center of the circle to any point on the edge.
Now let's think about the sum of the forces
action in these directions. Newton informed us
that the sum of those forces on any object will
equal the mass of that object times its
acceleration. Are the astronauts accelerating
tangentially to the center of the space station?
Well, the space station is rotating at a constant
angular velocity, and the tangential velocity is
equal to the angular acceleration times the radius
of the space station (v_tan = ω*r). Since
the angular velocity isn't changing, the
tangential velocity isn't changing, and so the
their is no tangential acceleration. Likewise,
Jorge is running at a decent clip such that he
isn't moving with any angular velocity. As long as
he runs at a constant velocity, his angular
velocity doesn't change, and so his angular
acceleration is zero as well. The total force
acting on Fred and Jorge in the tangential
direction is consequently zero.
For something to change the direction in which
it's moving, it has to accelerate. So if there is
no net force in the tangential direction, there
must be a net force acting in the centripetal
direction (at least in Fred's case).
What do things look like in the centripetal
(centerpointing direction)? In the world of
things moving in a circle at a constant speed, it
happens that the acceleration in the centripetal
direction is equal to the square of the tangential
velocity divided by the radius of the circle
(a_cen = v_tan^{2}/r). Since
v_tan = ω*r,a_cen = ω^{2}*r. Fred
is moving at a constant angular velocity R. The
net force acting on Fred in the centripetal
direction is equal to Fred's mass times his
angular velocity squared times his distance from
the center of the space ship (F_net,cen,Fred =
m_Fred*ω^{2}*r). Jorge isn't moving
with an angular velocity, so the net force acting
on him in the centripetal direction is equal to
zero.
Centripetal sounds a lot like centrifugal, doesn't
it? That's no coincidence. While centripetal means
center pointing or toward center, centripetal
means away from center. Centripetal force is a
real force, centrifugal is fictional. To rotate
around in a circle at a constant speed, you have
to accelerate towards the center. That
acceleration is known as centripetal acceleration.
The feeling you have of being flung away is the
centrifugal force, which is just a consequence of
you being accelerated toward the center.
The two astronauts do not feel the same
centripetal or centrifugal force. Fred is
accelerating centripetally, and Jorge isn't. And
since they are getting their feeling of weight
from the centripetal force, Fred feels heavier
than Jorge, even though they have the same mass.
For more information about the difference between
the centrifugal and centripetal forces, check out
this website:
hyperphysics.
Keep questioning,

Answer 2:
I am picturing the astronaut doing something
similar to this move clip: watch
this video, except he should be running pretty
fast instead of walking. Let's call this Olympian
sprinter Jerry. If Jerry did indeed match the
angular rotation with his sprinting, he would no
longer experience centrifugal force.
What would happen to Jerry then? Since he is
essentially floating, the force of his feet
pushing on the space station as he tries to run
would send him towards the middle of the space
station. If he had nothing to grab on to or slow
him down, he'd float right on to the other side.
It's doubtful he'd reach the other side feet
first, so instead he'd bump into the spinning
space station at some odd angle. Since the space
station is moving pretty fast, he's in for a nasty
rug burn."
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