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37

The bus experiences considerable drag, and will therefore fall more slowly than a person inside the bus. The scenario is possible in principle - but after carefully viewing the clip and doing some calculations, I believe that the details are inaccurate. Assume the bus has a mass of 5000 kg (pretty light for a bus), and is 3 m wide by 3 m tall - so the ...


20

If the bus was in a vacuum (both inside and outside), then the passenger would float. However, the effects of air resistance on the two objects (passenger and bus) are probably not negligible in such an instance. The bus will be moving relative to the outside air, and so will be accelerating towards the ground at a rate less than $g$. If we then released ...


11

Earth moves around the Sun and the Sun moves around the galaxy and the galaxy moves with unknown speed and direction. We have speed so the mass of us all altered. The relativistic mass is altered, but this is a somewhat archaic term these days, and is said to be a measure of energy. Nowadays when we say mass without qualification, we tend to mean rest mass. ...


8

You seem to be groping towards the fact that the gravitational three-body problem is, in general, not solvable. We can get away with saying "the sun is at one focus of an elliptical orbit" in the solar system because the sun is so much larger than anything else around. The sun is 1000 times more massive than Jupiter, so the sun-Jupiter barycenter is about ...


6

Electrons in a conducting disk in order to maintain equilibrium will have to have a centripetal force on them equal to the local change in potential energy with respect to a change in radius, that is $$ m_e\omega^2 r = -e{d\phi\over dr} $$ After integrating, we get a potential difference between the center and a point R out $$ \Delta\phi = -{m_e\omega^2 ...


6

The rest mass of an object, by definition is the total energy of an object as measured by an inertial observer who is at rest relative to the object. If the object is not moving uniformly, then you can measure its rest mass from a momentarily co-moving freefall frame. This rest mass is also the constant in Newton's law, i.e. the inertial mass as well. So ...


6

At first, the bus and the person would accelerate at the same rate due to gravity. However, the situation is more complicated due to air resistance. The bus experiences air resistance as it falls. The person inside the bus experiences less air resistance because the air inside the bus moves with the bus. This means that the person does not experience as much ...


4

You use the term frame of reference but we need to be careful what we mean by this. In special relativity this phrase generally means an inertial frame i.e. a frame in which Newton's first law applies. In GR we obviously can't have a global inertial frame because objects accelerate (due to gravity) whenever they are near a mass so their behaviour isn't ...


4

Proper acceleration is acceleration away from following a geodesic. As such, it is $0$ if and only if the object in question is free falling. If there is any net non-gravitational force, then there is proper acceleration. Standing still on the Earth's surface is not free falling. The ground is preventing free fall, and proper acceleration is $g$. Note that ...


3

You are asking us for the distance of the trip in the rest frame of the photon. The problem with asking that is that there is no rest frame of a photon. A photon can never be at rest, so it has no rest frame. This is like asking what a bowl of petunias thinks about its existence as it falls to the surface. A bowl of petunias doesn't think, therefore we can't ...


3

I suggest that it doesn't make much sense to say that the planets orbit the barycenter of the solar system. Beware that you are going very much against the grain of the best models of the solar system in writing that. All three of the leading ephemeris models (JPL's Development Ephemeris, the Russian Institute for Applied Astronomy's Ephemerides of the ...


3

No, no you guys (Except Floris and those who up-voted him) have missed an important observation... Look Carefully at the video again. At first the bus just tilts as the bridge bends. When the bus starts tilting (due to friction with the bridge it has not yet started falling) it has not yet obtained considerable vertical velocity. However as the man loses ...


2

We do have a rough idea of the relative speed and direction of our galaxy, with respect to the other galaxies around us, the so called local group. In general relativity, which is our best theory of the universe to date, there is no such thing as absolute speed, as it depends on which frame of reference you use to measure things in. Our Earth and the ...


2

The centripetal force is not a force that is required to exist, but rather a description of a force that would keep a particle in uniform circular motion. The only forces on the particle here are its weight and forces from other particles (modeled by the fluid density and the incompressibility assumption).


2

Here is one solution to Einstein's field equations: $$ds^2=dt^2-dx^2-dy^2-dz^2 \text{ on } \{(x,y,z,t):x,y,z,t\in\mathbb R\}.$$ It has a global coordinate system, a global reference frame, no closed time like curves, and a famous name, Minkowski space. Our second solution is a different manifold $\mathbb R^3\times \mathbb S$, which can (but doesn't have ...


2

You experience time normally always. You'll never notice that the world around you looks slow, or some such thing. What special relativity says is that other observers, observing a clock that is moving relative to them, will see that clock as moving slowly. You are never moving with respect to yourself, of course, so you always see "ordinary" time. ...


2

Although Mark Eichenlaub's answer is perfectly fine, I will post this answer, so that the time I spent writing it won't go to waste, and someone might find its detailedness useful. To understand what happens when you change back and forth between inertial and rotating reference frames, consider a conical pendulum. In an inertial frame you see that the ...


1

There is a nice thought experiment that explains this phenomenom, usually called the wire argument. I think you can find it in Feynman's lectures though I don't know who thought of it first. The set up is the following: let's consider a wire with zero total charge but with a current going through. For simplicity's sake, let's assume that the charge carriers ...


1

I didn't redo your calculations and I assume that they are correct, which actually doesn't play any role in what I'll describe now. Notice that in the second scenario the 2kg ball will inevitably start to move. By keeping it still you change the reference frame one more time, which invalidates the use of conservation laws. You cannot use the conservation of ...


1

Here's how I demonstrated this concept to my son when he was younger. Take a plastic bottle and put some pebbles or little toys in it. Then toss it in the air and catch it. If you look in mid-flight, you can see the little toys just floating around inside the bottle. But they're still at 1G. And when you look at this example, it's totally obvious what's ...


1

Fortunately, you don't need any special relativity or general relativity. All you need to describe orbital motions (to a high enough degree for NASA to use) is classical mechanics. The key in classical mechanics is that rotating reference frames are not inertial. The laws of physics as you know them only hold in an inertial frame. Over time scales of a ...


1

And while it is philosophically acceptable to just "know" that the speed of light is constant but it not to just "know" that it is invariant. Fixed constant values such as the mass of an electron or the spin set of an electron are things one can accept as given. Kind of: be careful. We can fix some of the fundamental constants by choosing covarying unit ...


1

Imagine a little piece of water on the top surface at radius $x$. The height of the water is $y(x)$. By moving inward $\mathrm{d}x$, the water would reduce its energy by $m g \mathrm{d}y = m g y' \mathrm{d}x$. It therefore feels a force of magnitude $m g y'$ towards the center. This force causes the water to accelerate towards the center. We know this to ...


1

Giving a full answer would take long, but here are a few steps to help you. The easiest is probably to start from the result, eq. (11). Multiply by a vector test function and integrate it over a given volume $V(t)$ within the solid phase, which is advected by the velocity $w$. Replace $w(x,t)$ by its value, defined in (3) -- note that $x_G$ has for ...


1

In general relativity there might not be a general frame of reference that will look the way an inertial frame of reference looks in special relativity. And the fundamental deep down reason is that we didn't assume there had to be, thus it didn't have to happen. Whether a particular solution to Einstein's equation has one or not is up to experiment to ...


1

But we also know that a perpendicular force always causes an acceleration according to the rule of addition of forces. All forces cause acceleration. Perhaps you mean specifically tangential acceleration (changes in speed)? If the centripetal force is greater the resulting vector is near the perpendicular, if the centripetal force is in perfect ...


1

First of all let's study an imaginary system where both the bus and the person are not subject to drag forces due to the air: If the person is not bounded to anything he will be subject to free falling and thus to a uniform acceleration $g$. Also the bus will be free falling and thus they fall together with the same velocity. If we take the drag forces into ...



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