# Tag Info

69

The Foucault pendulum is a great experiment which does demonstrate that the Earth is rotating, but it was only introduced in 1851. The Earth had been known to rotate for several centuries before that, probably stimulated by Copernicus and Galileo pushing the heliocentric model of the solar system during the 16th century. A couple of decades before Faucalt's ...

54

Foucault pendulum. I don't know how the ancients did it, but it is surely pure classical mechanics. The animation describes the motion of a Foucault Pendulum at a latitude of 30°N.

45

What luck! Just yesterday I was thinking about this exact same phenomenon whilst watching the film 'The Imitation Game'; the title sequence contained a moving tank, more on that later. When I was little, I used to observe this all the time; not in wheels however, but in caterpillar tracks: Notice how, when a segment of the track touches the ground, it ...

42

If you jumped "straight up", you would still have a horizontal component of velocity (relative to a nonrotating frame), so you would still end up coming "back down". Likewise, the shower water is moving horizontally in a nonrotating frame, which makes it collide with the floor eventually (since the floor is curving upwards in the nonrotating frame). But to ...

41

The sun does rotate. We can see the rotation of the sun by the doppler shift of the light we get from the sun. . (Image from this page.) Since we know the characteristic spectrum of light from a hot body of a given temperature, we can use the same effect to determine if other stars rotate as well. Note that this only gives the spread in velocities along ...

38

Barring whatever fantastic energies would be required to stop the mass of the Earth from rotating and then changing the direction of the rotation, one of the major things I can see changing would be the expectations of weather patterns. Part of what affects our weather is known as the Coriolis Effect. While there would certainly be effects from the ...

32

Yes, the sun and nearly all other stars do rotate. One can see the rotation of the sun by looking at the motion of sunspots on its surface. Over time, the sunspots will move across the sun's surface - proof of its rotation. Furthermore, the rate of the sun's rotation is not constant throughout the sun; it is higher near the equator and slower near the ...

20

Tsiolkovsky figured it all out more than 100 years ago :) Tsiolkovsky describes a cylindrical space ship: 100 meters long, 4 meters in diameter, rotating end-over-end about its "central transverse diameter", with an endpoint velocity between 1 and 10 meters per second, producing an angular velocity between (approximately) 0.2 and 2.0 rotations ...

19

The day/night cycle is the first obvious effect: Days and nights would both be longer (EDIT Or shorter, apparently I got it backwards) if the speed of rotation is the same. All life on the surface of the planet has evolved for day/night cycles of roughly the length we experience now, with leeway for the difference between summer and winter. A sudden ...

17

I think the Foucault pendulum is the best answer, but for the sake of variety I'll add another very interesting one: the equatorial bulge affecting the figure of the Earth. This is the "pancaking" of the planet due to its rotation. You can measure the geometry of the Earth without leaving its surface, and find that it is bulging in accord with your ...

17

Both are Euclidean isometries (distance and global-shape preserving maps): the only other kind of Euclidean isometry is a reflexion, although this last one is "discrete" - you can't have a fraction of a reflexion, whereas you can have a fraction $\alpha$ of a translation or rotation: you translate $\alpha$ times as far or rotate through $\alpha$ times a ...

15

The energy levels of a diatomic molecule are $E = 2B, 6B, 12B$ and so on, where $B$ is: $$B = \frac{\hbar^2}{2I}$$ Most of the mass of the molecule is in the nuclei, so when calculating the moment of inertia $I$ we can ignore the electrons and just use the nuclei. But the size of the nuclei is around $10^{-5}$ times smaller than the bond length. This ...

14

Anything related to the Coriolis effect (some pretty pictures can be found in the link), i.e. even cannons will be (not precisely, rather seem) deflected because of the earth's rotation.

14

Well, for the basics of the Foucault pendulum, this wikipedia page does an adequate job describing how it works (Specifically read up on the Precession as a form of parallel transport section). This page also has a nice explanation of how they work: A Foucault pendulum is just like any other pendulum, nothing more than a weight attached to a wire; but ...

13

An indirect indication that the Earth rotates is the fact that the rotation varies over time. First of all, the orientation of the Earth's axis changes: long-term effects like precession and slow variations in the axial tilt, as well as small short-term variations like nutation. Precession was already known in the Ancient world (Hipparchus, Ptolemy,...) and ...

13

Circular motion in special relativity is somewhat tricky: Note that for circular motion, the acceleration in the spaceship travelling in a circle is not zero, so the spaceship is not in a single frame of inertia. Here is an interesting thought: Distances perpendicular to the direction of motion are not subject to contraction. Hence, if the observes on ...

12

During the flight, you need to get up to use the restroom. There's one 10 rows in front of you, and another 10 rows behind you. Does it take longer to walk to the one that's moving away from you at 600 mph than the one that's moving towards you at 600 mph? No, because you're moving at 600 mph right along with it -- in the ground-based frame of reference. ...

11

This is a note on why angular velocities are vectors, to complement Matt and David's excellent explanations of why rotations are not. When we say something has a certain angular velocity $\vec{\omega_1}$, we mean that each part of the thing has a position-dependent velocity $\vec{v_1}(\vec{r}) = \vec{\omega_1} \times \vec{r}$. We might consider another ...

11

I prefer to think of it that the Earth and Sun actually orbit around their combined center of mass, which just so happens to be very deep inside the sun. The same can be said for the Earth-Moon system.

10

The answer, although I am not a geophysicist, is a definitive no. The main way we can tell that pole reversal happens is with the direction of magnetisation of ferrous ores. One looks at the magnetisation versus age in the ferrous ores and then dates the ore by standard techniques. From this we can deduce where the poles were relative to the particular bit ...

10

Firstly you need to understand Newton's law's. basically the second law. Concisely second law is :"whenever we apply a force on an object this force changes object's velocity's magnitude if it is in the same direction as that of the direction of motion and changes the direction of motion if the applied force is not in the direction of motion." When an ...

10

Your question will eventually lead you to Mach's Principle. It is an old, yet unsolved question, that still remains at the stage of "philosophical idea". I understand that your question is equivalent to "What would be found if we could measure all effects on the pendulum with infinite accuracy?", what if even the tiniest contributions could be registered? ...

10

Given the rather large volume of the universe, I suppose it's possible. Not as an initial condition as far as I can tell though because of the conservation of angular momentum. However, given the right circumstances of impact events on a rogue planet (with no other bodies to perturb its non-rotation), I suppose it's possible. Highly unlikely, but ...

10

You have fallen prey to a popular simplification of spinors. The statement "you have to turn electron by 720 degrees in order to get the same spin state" does not refer to an actual rotation of an actual electron. In quantum mechanics, we describe the states of objects as elements of a Hilbert space $\mathcal{H}$. The crucial thing is that not all elements ...

10

Consider a point $P$ on the surface of the wheel. If you look at the horizontal velocity of that point in the frame of reference of the wheel (axis stationary), then for a wheel of radius $r$ with angular velocity $\omega$ that point will have horizontal component of velocity $$v_h = r\omega\cos(\omega t)$$ The linear velocity of the wheel $v = \omega r$. ...

9

you wrote: "How can [the velocity of the contact point] be zero when it's in continuous motion?". However, you should keep in mind that motion is relative and therefore your question should be actually read as: "How can the velocity of the contact point be zero relative to the contact surface, when it's in continuous motion relative to its axis of ...

9

If you slow down, it will take you longer to type a sentence, won't it? When the Earth slows down (i.e. the speed of rotation is decreasing), it will take longer to complete a rotation, so the day is longer (i.e. the length is increasing).

9

Ah, good question. The radian is actually a "fake unit." What I mean by that is that the radian is defined as the ratio of distance around a circle (arclength) to the radius of a circle - in other words, it's a ratio of one distance to another distance. For an angle of one radian specifically, the arclength $s$ is equal to the radius $r$, so you get ...

9

The reason that you get slip at even the smallest forces results not from the fact that the tire is slipping against the ground, but that the tire is elastic. There is no way to completely eliminate slip with an elastic tire. Let's see why this is. To measure the slip, lets put twenty little green splotches of die evenly spaced on the circumference of the ...

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