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73

It sounds like your confusion is coming from taking paraphrasing such as "everything is relative" too literally. Furthermore, this isn't really accurate. So let me try presenting this a different way: Nature doesn't care how we label points in space-time. Coordinates do not automatically have some real "physical" meaning. Let's instead focus on what doesn't ...


53

The atmosphere rotates along with the Earth for the same reason you do. Force isn't needed to make something go. That's a basic law of physics - that a thing that's moving will just keep moving if there's no force on it. Force is needed either to make something change its speed, or to make its motion point in a new direction. A force can do both or just ...


40

Speed doesn't kill us, but acceleration does. When astronauts go into space at launch and when fighter pilots turn very tight turns at high speed they experience 'high g forces' - their bodies are accelerated very fast as they accelerate and gain speed to go into space or as the direction of their speed changes. One of the problems with this is that for ...


32

There are two separate questions there. The easiest one to answer is how we measure the velocity 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 ...


23

First: Maxwell's equations predict that the speed of light is absolute. The whole motivation for the special theory of relativity is to reconcile this with the notion that all motion is relative. In other words, you're worried about exactly the same thing that troubled Einstein. You just haven't understood how he solved it. The key to your confusion is ...


23

"A state of rest" is a relative term. Relative means - measured in comparison to the things around it. When you sit in a train and sip from a cup of coffee, you can do so because the cup is still relative to you even though both of you might be hurtling through the countryside at 200 km/h. For most experiments, objects can be considered "at rest" if they ...


21

Friction AKA wind resistance. You must have tried to stand in a strong wind or stuck you hand out the window of a traveling vehicle. From that you can feel the force that moving air exerts on objects in its way, and by Newton's law of reaction things in the way exert an equal force tending to move the air up to speed with the ground near it. Even if the ...


20

There are at least two reasons: the air layer adjacent to the Earth surface is dragged with it (being at rest with it). air viscosity -- it could be thought as a friction between different air layers. Upper layers are carried along by underlying layers. If the air were to stop suddenly it would result in ~1500 km/h wind speed. For comparison Hurricane ...


20

It all comes down to the fact that we are moving too. How can the bird drop down and catch the worm, if the earth and the worm are moving so quickly. It can because the tree, the bird, and the air are moving at the same speed, cancelling out. If we launch a spacecraft from Mars to the earth, the spacecraft is zooming around the sun at the same speed Mars ...


17

The fly does not slam into the windshield because at smaller scales of size, air effectively becomes much more viscous and halts its motion. A fly using a jet pack in a vacuum-filled car would slam into the windshield, however. Viscosity is a fascinating issue in terms of scale. Paramecia, for example, effectively must drill their way through water, not ...


16

Why should a high velocity kill you? The danger comes from acceleration, not velocity. Where you are in an airplane with a constant (but high) velocity, you feel nothing because the atmosphere of the plane is moving at the same velocity as you are, and because there is no net force or acceleration applied to you. However, acceleration is like a force for ...


13

Let me first go through this without friction or air drag. You say $v_y$ along the $x$-axis and the train moves with $v_x$ along the $z$-axis. This is a little inconsistent. I will use the velocities, but not your description of the axes. So the train moves in the $x$-direction, the ball is thrown into the $y$-direction and it the $z$-direction is up-down. ...


13

Velocity does indeed have to be measured relative to something. We can measure our radial velocity relative to any other astronomical object we care to, by measuring Doppler shifts. But if you want to know our velocity "relative to the Universe as a whole" rather than relative to any one object, we have to be a bit careful to define our terms. Because the ...


11

How can kinetic energy be proportional to the square of velocity, when velocity is relative? Without reading the rest of your question, I must first reply that one has nothing to do with the other. Kinetic energy is frame dependent, just as velocity is. Momentum is proportional to velocity and is frame dependent too, just as velocity is. Now, ...


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. ...


11

You are right in that the speed of light doesn't change. It is a completely different effect to the rain drop analogy. If you had only light hitting you directly from the front and directly form the back, you would observe the same intensity in the moving frame (only blue/red shifted). But for light coming at you from an angle $\theta_s$ in the rest frame, ...


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 ...


10

I endorse Ron's answer – it's the systematic way to proceed. The velocity $v/c$ may be written as $\tanh \eta$ where $\eta$, the rapidity or whatever, is the hyperbolic (Minkowski) counterpart of the (Euclidean) angle. The addition of velocities then boils down to an addition formula for $\tanh(\eta_1+\eta_2)$ because the rapidities just add additively. Let ...


10

The Earth is moving by 30 km/s around the Sun and relatively to the Sun. The Sun is orbiting the center of our Galaxy, the Milky Way, by the speed of about 200-250 km/s. Our Galaxy is moving relatively to the Local Group where it orbits and the Local Group falls toward the Virgo Cluster of Galaxies. However, the latter two velocities are small relatively to ...


9

I find the phrase "acceleration need not be relative anything" to be awkward, but I can see where it comes from. For the moment restrict our consideration the Galilean relativity (just to keep the math simple). Consider two frames of reference one ($S$) in which the body is at rest and another ($S'$) in which it moves with velocity $\vec{v'_i} = \vec{u} = u ...


9

At this stage, does the rocket still accelerate the craft? If by "velocity of the exhaust" we are talking about its velocity measured in the frame of the rocket, then Yes. Let $\mathbf u$ be the exhaust velocity as measured in the rocket frame, then in free space, the non-relativistic rocket equation is \begin{align} \frac{d\mathbf v}{dt} = ...


9

By my reckoning, if all speed is relative, then no mater how fast you go light should always race away from you at the same apparent speed. I.e. there should be no speed limit. If an invariant speed $c$ exists, then if an entity has speed $c$ relative to an inertial reference frame (IRF), the entity has speed $c$ relative to all IRFs. That's what ...


8

These days planes measure their speed (and position) using GPS. In the old days (my father used to fly Tiger Moth's!) they would measure air speed for a rough guide, but correct their speed by spotting landmarks on the ground. In poor visibility it was not uncommon for pilots to get lost, sometimes resulting in tragedy when they flew into mountains or ...


7

Have a look at http://en.wikipedia.org/wiki/Galilean_invariance. This is not too mathematical and explains what's going on. The basic idea is that there is no such thing as absolute motion. For example, because the earth is rotating as I sit here typing I'm moving at about 800 miles per hour. Why am I not splattered against my computer screen? It's because ...


7

You're dealing with an incomplete form of relativity. In the frame of the spaceship, nobody will notice anything different, since all inertial frames are equivalent In the "ground" frame, electricity would be moving at a different speed, by the relation $$\rm v_{e,ground}=\frac{v_{ship}+v_{electricity}}{1+\frac{v_{ship}v_{electricity}}{c^2}}$$ We cannot ...


7

Velocities in General Relativity can only be compared at a point, where local tangent planes coincide. Talking about the velocities of far-away stars in any sort of absolute sense is an empty question. Saying 'the coordinate velocity of Andromeda is 10^huge m/s' is, in a sense, not a statement about physics, but rather about your coordinate system. In ...


7

While you jump, just like earth, you continue to move in a circle around sun. This is simply because you and earth are both continuing to undergo a gravitational acceleration towards sun. However, while you jump, due to your and earth's difference in positions, earth and you will experience a miniscule difference in gravitational acceleration towards sun, ...


7

At low velocities like this you can ignore special relativity and simply add the two velocities. This is really easy to see if you imagine yourself standing still and the Earth moving under you. Relative to you the gun should fire just like you were standing still. This is called an inertial frame of reference. You see the bullet leave at $400\: ...


7

Your misconception has nothing to do with gravity - you're just getting a little mixed up about acceleration vs. relative acceleration. Let's dispense with gravity, since it's a red herring here. Say there are two cars. Car A accelerates at $+3 ~\rm m/s/s$ (to the right). Car B accelerates at $-5 ~\rm m/s/s$ (that is, to the left). So far, so good, right? ...



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