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60

You are right that, without a force acting on it, water falling from a tap could not follow a spiralled path. The tap, however, creates an illusion - the water appears to be spiralling, but it isn't - it's falling straight down. The illusion is created by the "turbine" inside the nozzle, which rotates the ring of spouts that the water falls through. The ...

10

First I just want to point out that saying that the four velocity $u_\mu$ satisfies $u_\mu u^\mu=-1$ is a convention, it is not a requirement. It amounts to a choice of the parameterization $\tau$. However, it is a very useful parameterization, it's not common to use other choices. In this parameterization, the four velocity takes the form ...

8

@innisfree's answer covers the tap in question, but I'd like to expand briefly. Like he says in his answer, without a force acting on it, water falling rom a tap could not follow a spiralled path Well, what if you do apply a force? Then yes, you can make water fall in a spiral. This picture is from a video I found while researching Chladni Plates. ...

7

Why is the scalar product of four-velocity with itself -1 The scalar product is invariant In the coordinate system in which the object is (momentarily) at rest, the only non-zero component is the temporal component. See that, in the rest frame, $\gamma = 1$ thus $d\tau = dt$. Then, (setting $c = 1$) we have \frac{dx^0}{dt} = 1,\,\frac{dx^i}{dt}=0 ... 6 This probably won't work in practice at all. First, there is the problem of Rayleigh instability that splits streams into droplets. It is true, that the more laminar the flow is, the more stable the stream. But in this case, the mechanism in the turbine will disturb the water rather than make it laminar, so the streams won't keep together in nice strings. ... 4 The derivatives with respect to \tau very much are numbers, but they are not all 1. Consider your worldline as a curve \gamma parameterized by \lambda. We have \begin{align} \gamma : \mathbb{R} & \to \mathbb{R}^4 \\ \lambda & \mapsto (x^0, x^1, x^2, x^3). \end{align} At any point in your worldline you have a position (x^0, x^1, x^2, x^3), ... 2 The coordinate velocity does indeed change discontinuously, but only if the acceleration changes discontinuously i.e. the jerk is infinite. Since for any physical system none of the time derivatives of position can be infinite, in a physical system the coordinate velocity can't change discontinuously. But let's ignore this for now and examine why we get a ... 2 Before the ball was thrown, it was already travelling at the speed of the train. When you are throwing it, you simply increase its speed by how fast you are throwing it. Keep in mind this does not work close to the speed of light. 1 It would be possible, and not even terribly difficult, to have a faucet whose stream, viewed at a moment in time, would appear as a spiral. A double-spiral diamond pattern would be harder, but should by no means be impossible, though unless the diamonds were rather coarse they would tend to become blobby as water moved away from the faucet. The key ... 1 Drift velocity is the velocity attained by a particle because of an electric field. Because current is proportional to drift velocity, which in a resistive material is, in turn, proportional to the magnitude of an external electric field, Ohm's law can be explained in terms of drift velocity. he definition of drift velocity can be understood by imagining ... 1 You need Newton's law of universal gravitation and Newton's 2nd law:\vec{F_g} = G \frac{M m}{r^2} \hat{r}\vec{F_{net}} = m \frac{d\vec{v}}{dt} Here, $M$ is the mass of particle G, $m$ is the mass of particle P, $r$ is the distance between P and G, and $\vec{r}$ is the unit vector pointing from G to P. If the only force on this particle is the ...

1

What affects would traveling at this speed have on the human body? The Earth revolves around the Sun at 18.5 miles per second and humans (as well as other living things) don't seem to notice. In addition, the Sun is travelling around the Milky Way at 143 miles per second. The astronauts and cosmonauts aboard the ISS are travelling at about 4.75 miles ...

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