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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 ...


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 ...


31

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 ...


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 ...


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 ...


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 ...


3

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 ...


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 ...


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 ...


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 ...


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

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 ...


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 ...


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 ...


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

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 ...


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 ...


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 ...


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.


1

It's a mistake to think of a body in orbit having its forces 'balanced' in some way - the forces are not balanced, because the body is accelerating towards the centre of the orbit! See my BBC article here, which explains this and weightlessness in general terms. I hope it helps. http://news.bbc.co.uk/1/hi/magazine/4625150.stm



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