New answers tagged

0

True weight actually the product of mass and gravitational acceleration which is equal to mg where the apparent weight is the sum of net forces ( when you standing in elevator and elevator is moving either upwards or downwards, either high speed or low speed then you feel your weight heavier or lighter this is the apparent weight that u feels which is equal ...


1

Time stops on the event horizon of a black hole according to a distant observer. One might consider Einstein'r original insight into relativity, where he realized on taking a street car that if the car were moving the speed of light he would never see a clock he was moving away from tick off its next increment of time. Something similar happens as one ...


0

Motion equations are independent from origin and kind of the coordinate system. What is the equations of motion? They are those relations that we can determine the position, velocity, acceleration, etc of the particle by using them. If the position vector of a particle in an inertial frame (coordinate system) be $\vec r(t)$ ($t$ is the time), we define a ...


2

The centrifugal force is a fictitious force which is why it does depend on the precise coordinate systems one uses to describe the mechanical phenomena. Imagine that you sit on a spinning carousel that spins at frequency $\omega$ around its vertical axis. According to a (nearly) inertial system of the people who stand on the Earth away from the carousel, if ...


1

What is meant is that physical laws are the same between (inertial) reference frames so that if you observe two bodies undergoing an elastic collision then you will experimentally determine that the momentum before the collision is the same as the momentum after the collision. An observer in another frame will also note that in his reference frame, the ...


3

The simplest answer, if I did not misunderstood your question, is to adiabatically compress the gas, both pressure and temperature will raise.


4

If you take a bottle of gas and carry it with you on a supersonic plane, then the molecules will go much faster without the temperature changing. If you let pressurized gas flow through a well-designed nozzle (De Laval nozzle), the gas will accelerate to supersonic velocity (i.e., faster than the original thermal speed of the molecules) while the ...


1

This is a really nuanced issue, but it is not the spinning space station that "causes" the centrifugal force, but the spinning frame of reference. We begin to say things like "he feels a centrifugal force on him" at a point where the *best reference frame to describe his motion is a rotating frame. You can model a system like your astronaut and a cylinder ...


1

does it also leads to ... No, it doesn't. A simple Counterexample: Consider the figure below (the bar $\textrm {AB}$ is on a plane parallel to $\textrm {xy}$ plane) We have $\Sigma \vec F=\vec 0$, but, if we calculate vector sum of torques about point $\textrm A$ we will obtain $\Sigma \vec M_A=F (\overline{AB})\vec k\neq \vec 0$ ($\vec k$ is the ...


17

If there is no atmosphere, and the station is a relatively smooth cylinder, you can indeed float there as the exterior walls spin around you (in the middle, or just above a wall, or anywhere). Now, suppose you start drifting towards a wall (maybe you threw your shoe the other way). You move towards the wall, but do not accelerate due to the rotation of the ...


34

You are correct in that if the astronaut is undergoing no translational or rotational motion relative to the centre of rotation of the space station the astronaut will feel weightless as in diagram $A$ and will not touch the space station. This is equivalent to jumping onto a rotating turntable with no friction acting. That feeling of weightlessness is due ...


46

Put a stationary astronaut in a small room inside a large spinning cylinder. After an instant walls of that room will hit him, and suddenly he will have the same velocity as the room. Due to angular motion, the room accelerates towards the axis of the cylinder. Subsequently, through the support force from the floor (the floor is at the surface of the ...


7

All you written is correct. Go further to the next point 4: once he comes to the cylinder wall and stands on it, he will get same angular speed as the cylinder, then he will also get centrifugal force and rotational gravity as in a film.


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By your assumption, we are talking about the FLRW Universe. Such a universe is by definition isotropic and homogeneous so there can't be any preferred direction at any point. If there were a difference between the CMB frame and the co-moving frame, it would indeed produce a preferred direction at some/most points (the direction of motion of one frame ...


0

As far as I understand your question, you can consider the Moon as continuously falling down to the Earth (or continuously following the moving Earth, if you want) due to the gravity. Nothing compensates gravity. However the problem is that the Moon aims not precisely into the Earth, but a bit away - that was original "error" from the Moon's first day. The ...


0

Lets distinguish 'rotation' into 'spin' (rotating around itself), and 'orbit' (orbiting around another object). The orbital motion is due to gravity. The 'centrifugal force' (instead of 'kinetic energy' of rotation, per se) is balanced by the 'gravitational force' [1]. The spin of an object doesn't need an external force (gravity from another object) to ...


1

Reichenbach's original volume, "Axiomatization of the Theory of Relativity", appeared in 1924. It is one of a long string of works that periodically rediscover and/or explore the issue of non-Einstein synchronization in Special Relativity. See for instance this review on "Synchronization Gauges and the Principles of Special Relativity" and refs. therein ...


1

Where is the spring balance here? It's not present. It's a statement that anywhere you find a force, you can put a spring balance along with it to measure the magnitude (at least conceptually). In this case, we might imagine that there is a solid radius present (like a rod), and a spring balance attached to the radius, free to move radially, but ...


0

A first problem is that there is in GR no such thing as "an observers frame", except in sloppy speech. There are various systems of coordinates. Two systems of coordinates may agree for an observer as much as one likes but differ elsewhere. And all the systems of coordinates are on equal foot, none is preferred. What could replace the "observer's frame"? ...


1

For the first part of your question, you have to realize that your net velocity (the one that you plug into the expression for centripetal force) is the vector sum of the surface velocity and your velocity relative to the surface. If you were running West as fast as the earth turns East, you would "stay in place" and the sun would appear to stop moving in ...


1

Yes. This can be done (and is done typically) using systems of pulsars, especially in 'Pulsar Timing Arrays'. See for example https://en.wikibooks.org/wiki/Pulsars_and_neutron_stars/Using_pulsar_timing_to_study_(and_navigate)_the_solar_system. Pulsars (specifically millisecond pulsars, MSP) can be incredibly accurate clocks. Relative motion between the ...


1

our aging is directly proportional to metabolism of body and division,growth and death of cells of body and if gravity has some effect on the rate of above aspects astronauts will be definitely younger


2

If I'm reading the question (v1) right, you present a paradox in paragraph 2 (commonly called Bell's spaceship paradox) and then try to resolve it in the next few paragraphs. Your resolution doesn't make sense, as pointed out in the comments. The mistake is that $u_2'$ is not zero, by the relativity of simultaneity: different observers will disagree on the ...


2

The first answer has all the results, but I will try to show some calculations, cause I have been writing them since there was no answer. It is known from General Theory of Relativity (GTR) that the closer you are to a massive object - the slower the time goes. On the other hand Special Theory of Relativity (STR) gives us the next statement: the faster you ...


4

This is anwered in Gravity on the International Space Station - General Relativity perspective, where we learn that time dilation in the ISS with respect to Earth equator is 1.00000000028655. So after 17 years for us, the astronauts would come back younger by about 0.15 seconds than if they have stayed on the ground. Note that a full GR treatment is ...


3

Temperature can be thought of as the vibration or oscillation of individual particles. More the vibration, more the temperature. The frames velocity is just the velocity of its mean position, as the vibration is independent of the frame velocity, so is the temperature.


0

Lots of questions! I'll try to get each of them: the object become infinitely heavy and requires infinite energy to move Light (photons) have no rest mass - ten, a hundred or a million times nothing is still nothing, so the (non-existent) mass isn't relevant - as you say further down. (Light does, counter-intuitively, have momentum, but that's ...


1

A ball of radius $d$ rolls (w/out slipping) on two surfaces. One surface moves with $v_1$ and the other with $v_2$ speed (in the same direction). The linear velocity of the ball center is the average velocity $$v_{ball} = \frac{v_1+v_2}{2}$$ and the angular velocity proportional to the speed difference $$\omega = \frac{v_2-v_1}{d}$$ These quantities are ...


0

we can also solve this using the concept of inertia. When we consider an accelerating train the velocity of the train continuously changes. The ball thrown upwards possesses the inertia of motion of the train. Hence at that moment when the train changes its velocity the ball continues to travel with the previous velocity of the train which is definitely less ...


-1

If apply in moving charge then no. Of forces act on them so we can't calculate position of charges but in case of static it is possible so it applicable only for point charge or static


4

You misunderstand special relativity. For objects that are moving at large speeds, the time runs more slowly for the object compared to the observer who measured the speed. To observe the motion of the object, you don't have to go to its coordinate frame and observe from there. You observe from the outside, that's how you measured the speed in the first ...


2

Let me explain light. Classically, light is electromagnetic radiation. There exists a field permeating all of spacetime called the electromagnetic field. Charges create curvature in this field. When charges accelerate, waves are created in this field. These waves are what we perceive as light. A little more specifically, let us examine Maxwell's equations ...


4

The Gödel universe is homogeneous and every observer anywhere in the universe observes the universe to be rotating around them. So a Gödel universe has no centre.


0

The hypothesis doesn't make much sense. The resistance of an object to being ripped apart is given by its elasticity, not by how much is massive. Anyway, to the central question there is no answer yet. This is the so called information loss paradox, one of the greatest unsolved problem in theoretical physics. In general relativity the object falls in a ...


1

I would suggest not using "relativistic mass". The strength of the concept is that it preserve non-relativistic formulae such as: $F = ma$ and $\frac{dp}{dt} = F$. which was valuable in 1916, but is dated in 2016. It's more productive to work in Minkowski space, where rest mass: $mc^2 = \sqrt{E^2-(pc)^2} $ is a four-scalar (the same in all frames), and ...


1

The first green part is the Rodrigue's rotation formula. The second green part is a small angle approximation for $\delta \theta$.


0

The train is doing work on the car, that is why its able to accelerate it to a kinetic energy of 200k Joules from the frame of reference of the ground without the need of the car engine burning more gasoline. Notice that you said that the train is already moving at 10 m/s, so this implies the train already has kinetic energy, and some of this kinetic energy ...


2

Interesting question. Taking a stab at it - not absolutely sure this is correct, but let the comments begin. In the frame of reference of Earth, the light travels straight out to the reflector, and straight back. You are asking about the case where an observer is in a reference frame that is moving with respect to Earth/moon, and the picture would have to ...


1

You are missing what Landau wrote before that part: "If we were to choose an arbitrary frame of reference, space would be inhomogeneous and anisotropic". If you choose an accelerating frame of reference, fictitous forces will be present and free bodies will start to move even if no force is acting on them. As Landau writes, you have to choose a frame in ...


0

In special relativity (things are a bit different in general relativity) time dilation is always relative. There is no such thing as an absolute velocity so there is no such thing as an absolute time dilation. If you are travelling relative to me at some speed $v$ then the relative rate at which I observe time passing for you is: $$ \frac{d\tau}{dt} = ...


0

When a top rotates, it rotates about its centre of mass. The centre of the mass is a point on the axis of rotation. Since the axis is also stationary as is the centre of mass, therefore all the points in the axis are eligible to be considered fixed about which the top is rotating. Besides,I would prefer to use the term axis instead of a fixed point.


0

It turns out you cannot use an accelerometer to determine the attitude of a rocket at any time other than when it is experiencing the normal force from the earth. This is explained in some detail in this article: Thinking About Accelerometers and Gravity. The key point from the article is this line: "An accelerometer never senses gravitational acceleration ...


0

I don't really know anything about Hawking radiation but one thing bothers me in this question. In flat spacetime, generators of boosts are Killing vectors (generators of isometries: the symmetries of spacetime itself). In curved spacetime there are no such Killing fields. You cannot boost your spacetime and get the same thing. It is not true that all frames ...


3

Any observer outside the Schwarzschild radius sees the same thing: matter approaching the Schwarzschild radius at slower and slower (asymptotically zero) speed, forming a thin shell around the event horizon. The matter takes an apparently infinite time to collapse, and infinity is infinitely larger than a large finite the same way it's infinitely larger than ...


3

Rotation of a 3-vector We'll find an expression for the rotation of a vector $\mathbf{r}=(x_1,x_2,x_3)$ around an axis with unit vector $\mathbf{n}=(n_1,n_2,n_3)$ through an angle $\theta$, as shown in Figure . The vector $\mathbf{r}$ is analysed in two components \begin{equation} \mathbf{r}=\mathbf{r}_\|+\mathbf{r}_\bot \tag{01} \end{equation} ...


2

The principle of relativity says that there is no experiment that can determine absolute motion. So all observers, regardless of relative motion, need to agree on the outcome of any experiment. Because to the relativity of observers' measuring devices, they may not numerically agree on the measurements. By applying the laws of relativity they will be able ...


0

The frictional forces try and reduce the relative motion between the water and the spheres. If the water is travelling faster than the spheres then the water exerts a frictional force on the spheres to try to make the spheres move faster and the spheres exert a frictional force on the water to try and make the water move slower.


2

Drag force opposes the motion of a body relative to the surrounding fluid. In this case the surrounding fluid moves to the right and relative to that the solids move to the left. The drag force is opposing the motion to the left, hence it is towards the right. The solids are being swept away by the fluid.


2

A few comments before doing the calculation: In the CM frame, there is only an attractive force, while in the given frame, there is both an attractive and a repulsive force. This is no more mysterious than the fact that a vertical object in my frame can look tilted to somebody with rotated axes. Going from the CM frame to your frame mixes the electric ...


4

Lorentz Transformations Suppose we call the lab frame the K-frame and a frame moving at velocity, $\mathbf{v}$, relative to the K-frame called the K'-frame. Then we can express the electromagnetic fields in the K'-frame in terms of the K-frame fields as: $$ \begin{align} \mathbf{E}' & = \gamma \left( \mathbf{E} + \boldsymbol{\beta} \times \mathbf{B} ...



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