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That's because the Centrifugal force that is created by the rolling counteracts gravity. If the pilot would do the roll over slower, the water would spill.


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Because this is exactly the same as swinging a bucket of water in a vertical circle. The water will not fall out, if it is swung fast enough. https://www.youtube.com/watch?v=Zjqrx7wrpJc source When you swing things around in circular orbits, it wants to fly "out of" the orbit. That is why water in the bucket is squeezing against the bucket which is the ...


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The underlying reason for OP's flawed argument is that a premature use of EOMs in the stationary action principle $$ S~=~\int\!dt ~L(r,\dot{r};\theta,\dot{\theta}), \qquad L(r,\dot{r};\theta,\dot{\theta})~=~\frac{1}{2}m(\dot{r}^2 +r^2\dot{\theta}^2) -V(r),\tag{A}$$ destroys the variational principle. Concretely OP is implicitly assuming that (3) is a ...


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Effective potential is defined by the formula $E=T_{radial}+V_{eff}(r)$. Your calculation shows that once you make this identification it is not true that $\mathcal L = T_{radial}-V_{eff}$, but that is fine. This happens because centrifugal term (i.e. the one with angular momentum) is really kinetic term and not a true potential. Hence it must enter the ...


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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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