New answers tagged

12

How can we detect Earth's spin? Apparent motion of Sun You will have observed that the sun reappears every 24 hours. There are two common explanations for this. One of them is that the earth rotates with a period of approximately 24 hours - this is the only explanation supported by the scientific evidence. The main alternative had a rather convoluted ...


2

Perhaps the least convenient but the most direct is go to the Moon and observe the Earth. The (average) length of day as measured by timing stellar transit to stellar transit, sidereal day, differs by 4 seconds from the length of day defined by timing noon on one day to noon on the next day, solar day. A satellite launched East requires less energy to ...


0

This is the whole reason why we call it 'relativity'! There is no global unambiguous way to define an absolute velocity, so only the relative velocities matter. Everything else is just from a point of view. When one says 'Bob moves at 10km/h and Alice is stationary' they are implicitly defining a reference frame. Usuallay in day to day life, we define our ...


1

let's assume we have 2 rays moving at 180°. If the container ( and the background ) move instead of the photons, the container would have to move in the direction of both rays. But, it's impossible since we assumed 2 antiparallel rays. How can container move forward and backward simultaneously.


2

Your question is the one that Einstein pondered for long time and from which Special Theory of Relativity was born. He wondered what could happen if you travel at the speed of light how would you see a ray light. The problem was that according to Maxwell's Electrodynamics, explained light as oscillating $E$ and $B$ vectors along space and time, so as a ...


1

Elementary particles do not have consciousness, individuality or volition. They follow the rules of the boundary value solutions of the quantum mechanical equations they obey. The relativistic quantum mechanical mathematics have zero mass particles moving at velocity c, and in all valid frames massive particles move at velocities less than c. It is the ...


0

Pseudoforce are real forces, i.e., they do everything a normal force would do. The problem with conservative nature is that if the observer is moving in a bizzare fashion so that somehow the curl of its acceleration becomes non zero, then the pseudoforce will be non conservative. For observer moving in one direction, force will be conservative and if you ...


2

1) why $a_c$ has to have opposite sign. $a_c$ is the centrifugal acceleration in the rotating frame experienced by the tennis ball. $$\vec{a_c} = (\vec{\omega} \times \vec{r}) \times \vec{\omega}$$ You’re answer for $\vec{a_c}$ gives the correct sign and magnitude. If you draw the vectors for $\vec{\omega}$ and $\vec{r}$ and apply the right hand rule ...


1

We won't be able to observe the light beam because photons don't interact with each other -- there is no way for light to bounce off the other photon so we won't be able to see it! Even if we imagine a particle travelling parallel to our path, both at the speed of light, if a photon were to bounce off of the particle, it could never reach our position ...


0

Intuitively the motion of a rigid body is split between, translation of the center of mass, and rotation about the center of mass. The intrinsic inertia about those two motions are the mass and the mass moment of inertia. To rotate a body about any other point away from the center of mass means that the center of mass has to translate in addition to the ...


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This is Wolfgang Rindler's "grid paradox", discussed on Wikipedia here and both proposed and resolved on this PDF by Rindler. Its resolution is the exact opposite of what you're saying; if you remember being "right" then you must have instead trusted the ground's perspective, not the train's. The problem is essentially that our notion of "rigid" does not ...


1

Gravity is acceleration. Einstein's equivalence principle says that gravity (with the vector pointing toward the center of the mass) is equivalent to actual movement with acceleration pointed "outward". That's why we observe gravitational blueshift. Now, blueshift means that the frequency of the photon received is increased as compared to its frequency at ...


1

Yes and no. Remember in special relativity whenever someone asks a question, they always are told to draw a spacetime diagram. The same thing happens in general relativity. If you want to see what is possible, consider drawing a Carter-Penrose diagram. For a black hole you can draw the event of a test particle crossing the event horizon. The past light cone ...


2

We generalize the result from the second answer you linked: $$\vec{L}=\sum_i \left(\vec{r}'+\vec{{r}_i}' \right)\times \vec{p_i}=\vec{r}' \times \sum_i \vec{p_i}+\sum_i \vec{{r}_i}'\times\vec{p_i}=\vec{r}' \times \sum_i \vec{p_i}+\vec L' $$ Now $\vec{r}'$ is some arbitrary vector, not just the vector to the center of mass. Thus when the system is moving ...


4

Let's assume for now that the item is in a circular orbit (just to keep things simple) The Gravitational Pull is counterbalanced by the Centripetal Force This sounds to me like a case of the anti-centrifugal brigage "correcting" a statement by replacing the word "centrifugal" with the word "centripetal" and, in doing so, turning the statement into ...


1

Draw a spacetime diagram. If time goes vertically then the worldline of A is a vertical line because the station is inertial. C also has a vertical worldline since C always moves to oppose the train. If the train is a glass train A and C are literally next to each, its like if you had stairs next to an escalator. Someone can stand on the stairs and talk to ...


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Looks like you are thinking that motion should be along the line on which the Net Force lies as well as in the direction of Net Force. This is not necessary. Force is only supposed to change the velocity of the body. The resulting velocity is not necessarily/always along the line of acceleration i.e, change of velocity. The Centripetal force create ...


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You are asking Special Relativity to answer questions about scenarios it is unable to describe. Special relativity is a theory of inertial frames of reference; frames of reference moving at constant velocity. Lets imagine we are person A. Person C steps onto a train but does not move relative to us. He is stationary and is therefore in the same inertial ...


4

I think the statement in your book is false. The reason why one feels weightlessness in a satellite orbiting the earth can be understood in two ways: In an inertial frame attached with some distant stars. In the non-inertial frame of the satellite. (Strictly speaking, all the explanation I am giving is preRelativistic.) Looking from the frame of distant ...


29

The statement: The Gravitational Pull is counterbalanced by the Centripetal Force is rubbish. The satellite undergoes a centripetal acceleration because it is acted on by the gravitation force. Some people call the force which causes a centripetal acceleration the centripetal force. So in such a case the gravitational force and the centripetal force are ...


1

In particle physics we continually go to the center of mass system for the interactions under study, because the mathematical expressions are simpler and Lorenz invariance assures that the results will be the same in whatever system one studies the interaction. Suppose we have an electron in a bubble chamber. This is a pion decaying into a muon and an ...


2

From the moving frame of reference, the rock is moving upward with an initial velocity of 4 m/s, and, at the end of the same time interval, it is moving upward at 1 m/s. But now, as reckoned from the moving frame of reference, the change in potential energy is going to be different. This is because the datum for potential energy is moving downward, so, as ...


1

You are ignoring the change in the kinetic energy of the Earth as it and the rock accelerate towards their common centre of mass. If the rock speeds up in your moving frame then the Earth slows down in the moving frame and you have to consider both changes for the energy to balance. Obviously the change in the Earth's kinetic energy is tiny, but you need to ...


0

The reason for the "apparent" confusion, is that you ere, inadvertently, changing the frame of reference! In addition, the formula you are using is not correct for the cases in question. The energy being calculated, is the energy required to make a change in velocity $$E = m(\Delta v)^2 \ were\ \Delta v = v - v_o$$ For the case "walking on ground" $v_o ...


-6

Because gravity works on you based on your distance from other masses. That changes little when you are at 30K', but measurably slightly less. This still forces your feet against the floor and friction coef. allows for traction. a Smart Academic answer would be because the "Captain has turned off the seatbelt sign". and you have legs. the energy came from ...


52

Due to momentum being conserved, when you accelerate yourself forwards relative to the plane, the tangential force you're applying to the floor will accelerate the rest of the plane backwards. Since the plane has a lot more mass than you, its velocity will not change by very much. Thus, an inertial observer who was initially at rest with respect to the ...


-6

You, and the air and everything inside the aircraft, are travelling at the speed of the aircraft, and your motion is relative to that. Lest there be turbulance, you would certainly no longer be moving relative to the speed of the aircraft, and you would be accelerated by the difference. That's why they have seat belts.


35

Kinetic energy is not invariant under Galilean transformations. To see this consider the following: In the rest frame of the plane you apply a force $F$ of 100N for one second to accelerate yourself to 1 m/s. During this time you move a distance $d$ of 0.5m so the work done is: $$ W = Fd = 100 \times 0.5 = 50\,\text{J} $$ This of course is equal to your ...


1

Let's say you are doing a typical SR experiment and you have Alice and Bob flying around in spaceships and such and you have each ship feeding you data. Things outside look one way to Alice and a different way to Bob because of their inertial frames. Let's say they're observing two supernovas and trying to determine their timing relative to each other, and ...


2

Boosting means you are changing a frame of reference; boosting frames doesn't imply any actual motion. When you talk about boosting, you are talking about changing the way you are observing something instantaneously. Acceleration on the other hand, is a type of motion inside a frame of reference. When you talk about acceleration, you are talking about a ...


0

I might use "boost" for a short burst (more like an impulse) and "acceleration" for a more prolonged burst - but both imply a force applied for a certain time in order to effect a change in momentum. I recommend you ask your professor for clarification. He/she must have had a particular application in mind. In the case of orbital mechanics, the calculations ...


0

In fact, it's easier than it seems. When gravity affects an object, his space-time is being curved by the mass of the one who provocates gravity. So, if time and space are being curved, the distance the object has to travel is longer, so it's his time. In conclusion, mass curve space-time, and, by curving space time, time appears, and last longer. I ...


1

Yes inertial forces are always defined to go through the center of mass. This stems from the definition of linear momentum. For a rigid body linear momentum is the sum of each particle mass and speed which yields the expression: $$\vec{L} = m \vec{v}_{cm} $$ Linear momentum is the total mass multiplied by the velocity of the center of mass. The net forces ...


0

I would answer "yes". The Couloumb force $qE$ changes, and here's why: In frame at rest B=0, while in the moving frame (') B' is not zero. Since $E^2-B^2$ is Lorentz invariant: E' must be larger than E. (Which is the familiar relativistic squishing of fields--like in a transition-radiation-detector).


0

A real force has a reaction force. A pseudo force has no reaction force.


1

Real forces are those which arises due to actual interaction between objects.But pseudo forces are not result of any interaction between objects rather it arises due to change of frame of reference and that is why it is pseudo.For example let us consider a person standing in a lift and suddenly the lift is accelerated downward.Now you can see that from a ...


0

Yes. It can be shown that if the forces acting on the particles are PROPORTIONAL TO THE MASSES of the particles, then concerning force and torque, the forces are equivalent to a single force passing through the CM. An example that a force is proportional to mass is gravity. Therefore for particles under gravity, each particle is acted on by a gravitational ...



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