the pencil follows a straight line path as viewed from that external frame of reference. This is what Newton’s first law of motion guarantees because there are no longer any unbalanced forces acting on it. The pencil’s speed can be calculated from the ship’s rate of rotation in conjunction with the perpendicular distance of the pencil from the ship’s axis of rotation, while its direction will be tangent to the circle (or helix) it was following at the time of its release. That straight path will inevitably carry the pencil to the outside periphery of the spaceship (i.e., to its “floor”).
I’m still not convinced. Because the pencil does not loose its forward momentum.
If you are in a plane and you drop a pencil, the pencil will appear to go straight down.
If you are outside said plane you would see the curved trajectory, and that would be the same for our spinning space station
The plane flies in a straight line at a constant speed, say eastwards. While the pencil is released, it continues moving eastward at the same rate as the plane. So if you are inside the plane, you notice only its earth-ward motion, and not its eastward motion. This explains why the pencil appears to be falling straight down to an observer inside the plane. But if the same exercise was repeated while the plane briskly accelerated, it would look as if the pencil described a curved path while falling.
Since the space station is rotating it is accelerating continuously in the sense that it changes direction the whole time. When the pencil is released, it loses the centripetal force gluing it to a circular path around the hub of the space station. So it can no longer accelerate along with the rotating space station anymore and it flies off in a straight line, and eventually crashes into the floor somewhere different to where it was released. From the inside of the space station, it’s path looks curved, just like from inside of the accelerating plane.
When I first got my head around this years ago, I also spent much time drawing diagrams (or at least imagining them), in between pulling out my hair and so on.
I have always found mechanics and relative motion the most difficult aspect of physics, and indeed any science. Seems you need a particular kind of mind for it, that I apparently don’t have. Which is not to say you can’t understand it if you don’t have that kind of mind, but you will have far more difficulty understanding it.
When the ball is simply dropped from say h=1 m, the Coriolis force is relatively small because the velocity is small for most of the time of the fall. So, the deflection should be modest. I will try to estimate the amount of deflection. The centrifugal force is mg and is always radially out, choosing +y radially out, ay=-g+ayCor; I will argue that the ball does not acquire enough speed for the Coriolis force to have a significant radial component, so ayCor≈0, and y≈h-½gt2, vy≈-gt. So, the time to fall is approximately t≈√(2h/g)=0.45 s and vy≈4.4 m/s. The Coriolis acceleration, if the velocity is purely radial, points in the backward direction (to the left in my figure above) and would have a maximum magnitude of about 2v√(g/R)≈3.9 m/s2. If the ball drops almost vertically the Coriolis acceleration would be approximately ax≈2m√[(vx2+vy2)(g/R)]≈2mvy√(g/R)=2mgt√(g/R)=8.68t=dvx/dt; therefore, integrating, vx≈4.34t2 and x≈1.45t3. So, at t=0.45 s, vx≈0.88 m/s and x≈0.13 m=13 cm.
So the pencil would not have gained enough Coriolis effect to be deflected much.
In conclusion i don’t think you can berate the film makers to much.
A little more on it
To reduce Coriolis forces to livable levels, a rate of spin of 2 rpm or less would be needed. To produce 1g, the radius of rotation would have to be 224 m (735 ft) or greater, which would make for a very large spaceship
You may well be right. I’ve always found it useful to pick an appropriate frame of reference that allows the various motions to be described as simply as possible. Of course, it takes some practice to recognise such, and one could still argue that there’s the “right kind” of intuition involved in selecting such a frame to begin with.
My goodness, that physicist certainly knows how to complicate things inordinately! That’s not to say those answers are wrong, merely far more confusing and convoluted than they need to be. There is a far simpler and clearer approach. Once again, I urge you to do the exercise yourself, rather than relying on vague hand-waving such as “the Coriolis force is relatively small” and “the deflection should be modest”, followed by an approximation of dubious worth. Nothing beats a precise formulation because the Coriolis effect isn’t limited to letting go of a pencil close to the outer edge of a rotating spaceship. Its reach is considerably wider than that.
ETA: The ISS is a bit smaller than that 440+ metre diameter suggested by Wikipedia.
To reduce Coriolis forces to livable levels, a rate of spin of 2 rpm or less would be needed. To produce 1g, the radius of rotation would have to be 224 m (735 ft) or greater, which would make for a very large spaceship
Perhaps, once you have lived in such an environment for a while, you’ll get used to the Coriolis effect. Back on Earth, you’d need to adjust all over to the “normal” world again.
That’s no doubt true, but it wouldn’t obviate the appearance of weird counterintuitive motions that prevail in a Coriolis environment.
In any case, the interested reader can get a sense of this weirdness the next time s/he encounters a merry-go-round: Set it spinning at a good clip, hold on facing the centre post, and swing one leg as if attempting to kick the centre post.
One can imagine that in the future, people may grow up in such an environment, and perhaps end up with very different physics intuitions than ours.
In any case, the interested reader can get a sense of this weirdness the next time s/he encounters a merry-go-round: Set it spinning at a good clip, hold on facing the centre post, and swing one leg as if attempting to kick the centre post.
'Luthon64
Or let one person stand in the middle, and another on the edge, and then try tossing a ball to each other.
I’ll make a point of going on my next merry-go-round ride sober. As a rule, I can totally relate to Tolla’s analysis of the centripital trajectory of vomit. :-X
