Velocity transformation Definition and 20 Threads

Good evening, I was wondering about how velocities transform when two successive rotations are applied. In other words, how is the transformation law between two frames which are rotating relative to another. Lets say some particle is moving with a velocity v in an inertial frame S. If we go...

1. The 2nd line on the 3rd page of your notes, you have x=ct and x'=ct', thus ux=dx/dt and ux'= dx'/dt' =c according to Einstein's assumptiuon. 2. But near the end of the last page, you wrote dx'/dt' = (ux -v)/(1-vux/c2) . Compare with 1. This equation can be valid only for ux=c and...

I have used velocity transformation ibut a little confused on it so do solve the problem

I'm reading modern physics, Tipler 5th edition, pages 21 and 22, and I'm not understanding how the differentiation was done from the position to find the velocity. Equation for position: x'= y(x - vt) y is the gamma constant. Then in the first step to find the velocity, a derivative was done...

Homework Statement How to obtain the famous formula of velocity transformation using a chain rule. I know that there is a straightforward way by dividing ##dx## as a function of ##dx`## and ##dt`## on ##dt## which is also a function of them. But I would rather try using the chain rule. Homework...

Homework Statement Given: An object at rest with respect to an inertial reference frame S. 2 other inertial reference frames S' and S''. S' has velocity (vx, vy) = (-.6c, 0) with respect to S. S'' has velocity (vx, vy) = (-.6c, +.6c) with respect to S. Assumptions: If I transform my...

Homework Statement . An atom at rest can undergo radioactive decay, ejecting an electron at a maximum speed of 0.5c. If the atom in a particle accelerator is observed to produce an electron traveling at 0.75c, at least how fast must the atom itself have been moving? Homework Equations u0 x...

I cant't figure out how to transform ##\dot{r}##, ##\dot{\theta}##, ##\dot{\phi}## in spherical coordinates to ##\dot{x}##, ##\dot{y}##, ##\dot{z}## in cartesian coordinates (the dot is Newton's notation for the first time-derivative which is the angular velocity and velocity). I have no...

Homework Statement Two rockets A and B are moving away from the Earth in opposite directions at 0.85c and -0.75c respectively. How fast does A measure B to be travelling? Now I have worked out v = -0.85-0.75/(1- -0.85*-0.75) = -0.997. This is correct. Now I would like to work it out backwards...

Homework Statement A train travels in the +x direction with a speed of β = 0.80 with respect to the ground. At a certain time, two balls are ejected, one traveling in the +x direction with x-velocity of +0.60 with respect to the train and the other traveling in the −x direction with x-velocity...

Let S be the frame where the Sun is at rest. Imagine light from the North Star reaches the centre of the Sun, and let's define the equatorial plane as the plane that is perpendicular to this light and cuts the Sun into two hemisphere. Suppose a distant star A is on this equatorial plane and its...

I'm being asked to derive the velocity transformation between vy and vy' and my result isn't exactly matching my goal but I don't know what I'm doing wrong. It's an introductory modern physics course and we're covering special relativity. Assume a reference frame S' moving in some constant...

Homework Statement Two spaceships are moving away from Earth at a speed of 0.8c, with one ship following in the flight path of the other. Their separation along the axis of their motion is maintained at 0.1 light years as measures by the spaceships' instruments. A crew exchange vehicle is...

An observer on Earth observes two spacecraft moving in the same direction toward the Earth. Spacecraft A appears to have a speed of 0.50c, and spacecraft B appears to have a speed of 0.80c. What is the speed of spacecraft A measured by an observer in spacecraft B?So if S is the reference...

Homework Statement Consider a light signal propagating in some arbitrary direction, with vx \neq 0 vy \neq 0 vz \neq 0 and vx2 + vy2 + vz2 = c2 Use the Lorentz transformation equations for the components of velocity to show that v'x2 + v'y2 + v'z2 = c2 Homework...

Homework Statement Prove the law of transformation of velocities \begin{array}{l} {v_x} = \frac{{{v_x}^\prime + V}}{{1 + {v_x}^\prime V/{c^2}}}\\ {v_y} = \frac{{{v_y}^\prime }}{{\gamma (1 + {v_x}^\prime V/{c^2})}}\\ {v_z} = \frac{{{v_z}^\prime }}{{\gamma (1 + {v_x}^\prime V/{c^2})}}...

Homework Statement the particles in a high energy accelerator experiment are approaching each other head on, each with speed of 0.9520c as measured in laboratory. what is the magnitude of the velocity of one particle relative to the other? Homework Equations vx = vx' + u / 1 + (uvx' /...

Hi, I'm struggling with a special relativity question Two particles are traveling in an inertial frame in perpendicular directions to each other at velocity v. Calculate the velocity of each particle relative to the other I'm not sure how to approach it. In the past any velocity...

Let observer O' move respect to observer O with velocity V. Suppose, that O sees an object M moving with velocity v. A standard vector formula for velocity v' of the object M seen by observer O' is attached. My question is the following: suppose that the velocity v and v' are given. What is...

When textbooks derive the transformation of the Y(Y') component of the velocity of a particle, take into account that y=y' and use the time transformation depending only on the X(X') component of the parfticle's velocity and on the relative velocity as well. Please tell me why?