Velocity transformation Definition and 20 Threads

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion (e.g. 60 km/h to the north). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.
Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object has a changing velocity and is said to be undergoing an acceleration.

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  1. T

    I Velocity transformation between frames rotating relative to one another

    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...
  2. alhuebel

    I Constraints on Lorentz Velocity Transformation

    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...
  3. Zeeshan Ahmad

    Understanding Velocity Transformation

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

    I Relativistic Velocity Transformation: Diff. Operator Explained

    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...
  5. A

    Velocity transformation using the chain rule

    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...
  6. M

    Trouble with 2 step velocity transformation in SR

    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...
  7. D

    Modern Physics question -- an atom ejecting a relativistic electron

    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...
  8. Stollaxel Stoll

    B Velocity transformation from spherical to cartesian coords

    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...
  9. R

    Relative Velocity of Two Rockets and the Earth

    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...
  10. Lito

    Special Relativity -- Velocity transformation

    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...
  11. H

    Transformation equation of velocity contradicts stellar aberration?

    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...
  12. M

    Lorrentz velocity transformation

    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...
  13. S

    Special Relativity - Velocity transformation problem

    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...
  14. A

    Lorentz velocity transformation problem

    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...
  15. J

    How Do Lorentz Transformations Affect Light Signal Velocities?

    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...
  16. zimo

    Using rapidity - prove velocity transformation equations

    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})}}...
  17. P

    Lorenz velocity transformation

    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' /...
  18. M

    Special Relativity Velocity Transformation

    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...
  19. D

    What is the relative velocity of two observers with given object velocities?

    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...
  20. B

    Understanding Velocity Transformation: A Crucial Factor in Particle Motion

    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?
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