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In your scenario, your 3 statements are correct, and if nothing changes, your astronaut will not move from its spot as the wall of the cylinder moves past him. However, if somehow the astronaut "attaches momentarily" to the cylinder wall (the floor), then he will acquire the tangential velocity of the spot he attaches to, and this tangential velocity is ...

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Motion equations are independent from origin and kind of the coordinate system. What is the equations of motion? They are those relations that we can determine the position, velocity, acceleration, etc of the particle by using them. If the position vector of a particle in an inertial frame (coordinate system) be $\vec r(t)$ ($t$ is the time), we define a ...

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The centrifugal force is a fictitious force which is why it does depend on the precise coordinate systems one uses to describe the mechanical phenomena. Imagine that you sit on a spinning carousel that spins at frequency $\omega$ around its vertical axis. According to a (nearly) inertial system of the people who stand on the Earth away from the carousel, if ...

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This is a really nuanced issue, but it is not the spinning space station that "causes" the centrifugal force, but the spinning frame of reference. We begin to say things like "he feels a centrifugal force on him" at a point where the *best reference frame to describe his motion is a rotating frame. You can model a system like your astronaut and a cylinder ...

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If there is no atmosphere, and the station is a relatively smooth cylinder, you can indeed float there as the exterior walls spin around you (in the middle, or just above a wall, or anywhere). Now, suppose you start drifting towards a wall (maybe you threw your shoe the other way). You move towards the wall, but do not accelerate due to the rotation of the ...

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With no air, you are correct. The air makes this entirely different. I don't recall mention of there being heavy winds near the surface, meaning that the air is moving with the cylinder. The air is accelerating outward ("downward"), and the dragonfly would be accelerated with it. Along the hub, the air would not be moving much, and there would be a ...

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You are correct in that if the astronaut is undergoing no translational or rotational motion relative to the centre of rotation of the space station the astronaut will feel weightless as in diagram $A$ and will not touch the space station. This is equivalent to jumping onto a rotating turntable with no friction acting. That feeling of weightlessness is due ...

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Put a stationary astronaut in a small room inside a large spinning cylinder. After an instant walls of that room will hit him, and suddenly he will have the same velocity as the room. Due to angular motion, the room accelerates towards the axis of the cylinder. Subsequently, through the support force from the floor (the floor is at the surface of the ...

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All you written is correct. Go further to the next point 4: once he comes to the cylinder wall and stands on it, he will get same angular speed as the cylinder, then he will also get centrifugal force and rotational gravity as in a film.

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If a body of mass m hanged on a string is moving, let uniformly, on a circle fixed relatively to the ground, then an observer G on the ground uses the 2nd Newton Law : $$\mathbf{F}=m\cdot \mathbf{a} \tag{01}$$ and finds the relation between the force $\mathbf{F}$ and the acceleration $\mathbf{a}$. For observer G there exists a "real" force, the tension ...

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Note that you have to swing the pail with a certain minimum speed for the water to stay in. That minimum speed is such that when the pail is at the top of the arc, the rope accelerates the pail downward faster than gravity accelerates the water downward. Otherwise, the water falls out.

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If water particles move in a circular path its because of some net force towards the centre. This net force is usually called "centripetal force". Don't ever put centrifugal force into the description. It is not a force, but just a name of the "feeling" that your body (or in this case water particles) want to move out of the circular motion but can't.

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