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47

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 ...


17

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 ...


15

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 ...


15

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 ...


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. ...


12

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

Since the Lorentz transformations are a consequence of the postulate of constancy of the speed of light, together with some homogeneity and parallel postulates, it is a little difficult to make precise the request for a Lorentz-transformation free demonstration. But I will interpret the question as asking for a synthetic proof of the addition of velocities. ...


9

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 ...


9

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, ...


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} = ...


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 ...


8

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 ...


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\: ...


6

Key is to notice that your steps provide you with a unit length as well as a unit time. So, let's measure distance in $steps$ and time in $ticks$, with your speed being $1 \ step/tick$. The length of the train is $x$ steps, and its speed is $v \ steps/tick$ ($v<1$). It follows that $$x \ + \ 18 \ v \ = \ 18 $$ $$x \ - \ 11 \ v \ = \ 11 $$ Adding 11x ...


6

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 ...


6

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} ...


6

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 ...


6

If a plane is flying without any rudder input, then the banner will always fly straight behind the plane, with nose-tail-banner in a straight line, no matter what the speed or direction of the plane and/or wind. The only thing that affects the plane and banner is the flow of air over the control surfaces. How would the banner know that there was wind ...


6

We have to be careful in stating exactly what we're going to allow ourselves to assume here. We need some sort of principle of relativity -- that the laws are the same for both observers. But we don't want to assume anything else a priori, right? For instance, we don't want to assume at first that rulers have the same length for both observers -- we need to ...


5

The thing you throw in the air is also traveling at the same speed you are, in the same direction. When you throw it up, it doesn't matter that the earth below is moving backwards at speed, nor that the moon is moving past even more quickly, nor that the earth itself is spinning and moving relative to the sun. The ball has a speed and direction and ...


5

Yes, the ball would land in exactly the same spot, whether robot or person. The air does not remember the original speed, and new air coming in does not keep its velocity, but settles down with the co-moving air. The speed it has is determined by the fan blowing it in, not by the speed of the train. The reason is that the train pushes the air just as it ...


5

The early universe was a hot, high-friction environment in which solid objects couldn't form, and even if one had, it would have been kept at rest relative to the Hubble flow because of friction. Much, much later, stars, solar systems, and other structures began to form by gravitational collapse. There is a kind of scale-invariance in this collapse. What I ...


4

Assume that you jump straight up, standing on the equator. As soon as your feet leave the ground, you are in a highly elliptical orbit around the center of the earth. At that point you have the same angular velocity as the point you jump from. As you rise toward your one and only apogee, conservation of angular momentum requires that your angular velocity ...


4

The velocity of the rocket is irrelevant. The rocket can be considered as a frame of reference from which the exhaust gases are ejected at a certain speed - therefore the exhaust gases will always move away from the rocket at the same speed. If the rocket keeps producing thrust then it will keep accelerating, and the gases will keep moving away from the ...


4

This is quite straightforward as long as you break it up into steps. Let the tortoise travel with speed $v_t$ and Archilles with speed $v$. We split up the steps Archilles takes as \begin{equation} d_A = d_0 + d _1 + ... \end{equation} where $d_i $ is the distance travelled in a single step. The initial distance $d_0 $ is then just the initial separation ...


4

Your friend is correct. The acceleration of the projectile is determined by the thrust its rocket motor can produce. If the acceleration of the projectile is $2g$ then the thrust of its motor would be $2mg$. But launching the projectile from your space vehicle can't increase it's thrust. You can increase its initial velocity, but once the projectile has ...


4

No, the ball does not land in exactly the same spot, even in the absence of any air at all. However, in the real world, the effects in the train are probably too small to observe without a careful experimental setup. dmckee's answer describes physics in an inertial reference frame. However, because the Earth is spinning, the ball experiences a ...


4

Suppose two light pulses are released from A and B in opposite directions at the same time. Clock A’s timer will read 0 and clock B’s timer will read 0 at this instant. Now they both measure the time it takes until they receive a light pulse. Let’s suppose B measures 5 seconds for the pulse to get from A to B. Now I will assume the clocks of both A and B ...


4

If you're standing on the equator then you're moving, along with the earth's surface, at about 1,000 miles per hour. So if you fly up e.g. 100 meters with your jet pack you're still moving sideways at the same speed so the spot you took off from remains below you. Well, not quite. Because you're 100m above the surface you're moving in a circle that has a ...



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