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29

There are two separate questions there. The easiest one to answer is how we measure the vleocity of the Earth, Milky Way etc, because we measure it relative to the cosmic microwave background (or CMB). If you measure the CMB in all directions and find it's the same in all directions then you are stationary in comoving coordinates. However if you find the ...


10

There are a number of different frames of references. For the velocities of celestial objects we use: (i) The geocentric frame: This is a velocity measured with respect to the Earth's centre. Obviously this is quite useful for artificial satellites, but also for things like meteors. (ii) The heliocentric frame: this is the velocity as seen from the centre ...


9

In general relativity, angular motion actually does have some "relativity" to it as well. When you're in close proximity to a spinning object, you'll actually be dragged along with it. This is known as the Lense-Thirring effect, or just "frame-dragging". The most dramatic example is the ergosphere of a spinning black hole, a region where no object can remain ...


7

Suppose you and I start on the equator, a kilometre apart, and we both head exactly due North in a straight line, so we head off in exactly parallel directions: Now we know that in Euclidean geometry parallel lines remain the same distance apart. But if you and I measure the distance, $d$, between us we find that $d$ starts off at 1km but decreases as we ...


5

Careful with comments like "when he receives it"--simultaneity is relative, different frames will disagree about which reading on your clock happens "at the same time" that he receives the pulse. If he is 10 light years away in the frame where you were initially at rest, and you wait 10 years after sending the signal to fire your rockets, then you fire your ...


4

Let's do some math, shall we? Let's call $t$ the time as measured from Earth, and let's say your engine is running with acceleration $a$ for $0 \le t \le T$. The proper time, that is, the time as measured by a clock on a ship, is given by $\tau = \int_0^T \sqrt{1-v^2/c^2}\ dt$, where $v$ is the velocity as measured from Earth. Newton's second law for ...


3

The site rules forbid us from giving the answers to homework problems, but this problem illustrates a fundamental issue in relativity so I think it's worth some general comments. Incidentally you may be interested to read the Wikipedia article on the ladder/barn paradox, though in it's efforts to be comprehensive I think the article gets a bit confusing. ...


3

The Coriolis force $\vec F_{\text{coriolis}} = -2m \, \vec \omega \times \vec v$ only depends on velocity. The centrifugal force $\vec F_{\text{centrifugal}} = -m \, \vec \omega \times (\vec \omega \times \vec r)$ only depends on position. Finally, if the object is not rotating uniformly ($\dot {\vec \omega} \ne 0$), then yet another fictitious force comes ...


3

Now, why do the objects falling towards the Earth move along the geodesic paths with no acceleration? A body in a free-fall moves with acceleration g, so, why is it written like that? To understand the passage, we must make two crucial observations. (1) To person at rest on the Earth's surface, a free-falling object is accelerating towards the ...


3

The reason why both A and B can see each others' clocks running slow with no contradiction can be seen by studying this diagram (from this article): This shows two spacetime grids, corresponding to two reference frames moving at a constant velocity relative to each other (related by a Lorentz transform). Let the black, right-angle grid $(x, t)$ be ...


3

Speed is a distance (separation between two well defined points in space) traveled over a time. The speed of Earth you quote is the orbital velocity. We know how far away the Sun is and we know the shape of the orbit, so we know how far the Earth travels relative to the Sun (distance) per year (time). Likewise the speed of the Milky Way is also given ...


2

I believe you want to replace mass with charge and angular velocity with the magnetic induction. The Coriolis effect is an apparent force due to the fact that the observer is measuring with respect to a rotating frame of reference. There is no actual force acting on the body, so this can be made to disappear by changing the frame of reference. Classical ...


2

Newton's describes his notion of absolute time and space his Scholium on Time, Space, Place and Motion. In Newton's time, civil time was still measured by the motion of the Sun. Newton needed to distinguish time as measured by a sundial from the time as measured by a clock (or by the motions of the planets, or of Jupiter's moons). Scientists in Newton's day ...


2

It's reconciled by the relativity of simultaneity. Each observer is assumed to measure the time of events using local readings on a network of clocks at rest relative to that observer, which are defined as "synchronized" in that observer's own rest frame using the Einstein synchronization convention. But because this convention is based on each observer ...


2

Look in Wikipedia http://en.wikipedia.org/wiki/Coriolis_effect. For understanding intuitively the Coriolis force effect, assume an object moving according to a static (inertial) frame of reference, in the plane perpendicular to the rotation axis, and along the radius, In the rotating frame, see the animation in Wikipedia, the Coriolis force imposes an ...


2

I see what you're trying to ask. Let me try to rephrase it: Does an observer at the bottom of a massive gravity well perceive that the clocks of actors outside of the gravity well move faster? The answer is yes, but the intensity depends on the depth of the gravitational well. For anyplace far away from exotic things like event horizons and perhaps neutron ...


2

The discussion is mostly semantic. They are both calculated relative to a point, in the case of the torque the point has the additional meaning that if you put an axle trough the point, the object will start to rotatte around it if the net torque is not zero. It happens also that the torque will be the same if you chose any other point along the axis ...


2

My guess would be that $\mathbb E^n$ denotes Euclidean space. In addition to having geometric structure (angles and distances) and motions (rotations, translations, reflections) - not all of it terribly useful in the 1-dimensional case - it is an affine space. Affine spaces have no notion of distinguished origin or zero point. We can use a vector space like ...


2

Your first sentence is not true. There is a whole family of freefall frames that are co-incident at any spacetime event. They correspond to different "initial velocities" as they diverge from that event: in geometric language, their origins follow the many different geodesics defined by different tangent vectors of the tangent space at that spacetime event, ...


2

In relativity there is no absolute speed because there is no notion of absolute space or time--your speed can only be measured relative to some reference frame (a coordinate system which assigns a position coordinate to each object at each time coordinate), usually an inertial frame (the speed of a light ray is the same regardless of which inertial frame you ...


1

I can't quite fathom the source of your confusion (I think it might have something to do with a focus on the notion of rotation here---angular momentum does not require rotational motion), so I'm having trouble writing a really clear response. For the moment I would rather offer a program for practicing the right skills rather than reinforcing the mistaken ...


1

I was doing a question about if a train fits in a tunnel. Did the question assignment include a specific consistent definition of what's meant there by "to fit", in the first place? Presumably, in the setup which is typically considered, the ends of the tunnel (say participants $A$ and $B$) are supposed to be at rest to each other, the ends of the ...


1

You say: But for the observer on the planet, since the total angular momentum of the star about its axis is zero it should remain zero. But the observer on the planet does not occupy an inertial frame. An observer in a rotating frame measures fictitious forces. So there is no reason why angular momentum should be conserved.


1

Tilting an object in space changes its apparent dimension (think of trying to get furniture through a door: the width of an object depends on its orientation). Objects in relative motion are tilted in space and time (or rather, spacetime), and different observers will see things unfold under different perspectives. Personally, I find relativity of ...


1

The only outright requirement is that you compute all the angular momenta in your problem around the same center (modulo applying the parallel axis theorem to break the angular momentum of extended bodies into of-and-around the CoM parts). So you can freely chose any single point to use Now, as with most such "free" choices in physics there are generally ...


1

That's a very common misunderstanding of classical mechanics. The theory doesn't make ANY statement about the microscopic structure of space or time, it only makes a number of symmetry statements. The mechanistic view of what the theory "means" is a philosophical construct completely external to the theory. It's metaphysics, not physics. Time, in the ...


1

Other answers are good, but let me just try and give you something intuitive. First assume light travels the same speed in all frames of reference. So build a clock like this. A photon bounces up and down between two mirrors. This makes a clock, obviously. You could call the time it takes to make N round-trips one second. OK, you are A and you have such a ...



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