Fixed and Moving Reference Frames for adding speeds

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SUMMARY

The discussion focuses on the addition of velocities in different reference frames, specifically in the context of a planet gear's motion. It clarifies that the velocity of the planet gear relative to its carrier is calculated by subtracting the carrier's velocity from the planet's local velocity. The conversation highlights that while the Galilean transformation provides an approximation for small relative velocities, the Lorentz transformation is necessary for higher velocities, emphasizing the empirical derivation of these concepts.

PREREQUISITES
  • Understanding of Galilean transformation
  • Familiarity with Lorentz transformation
  • Basic knowledge of rotational motion
  • Concept of relative velocity
NEXT STEPS
  • Study the mathematical derivation of Galilean transformation
  • Explore the implications of Lorentz transformation in high-velocity scenarios
  • Investigate applications of relative velocity in mechanical systems
  • Learn about the effects of rotational motion on velocity calculations
USEFUL FOR

Physicists, mechanical engineers, and students studying kinematics and dynamics who seek to understand the complexities of velocity addition in different reference frames.

bugatti79
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Hi Folks,

I have some misunderstanding how one can add velocities of different coordinate systems.

Consider a planet gear rotating about its own axis and also rotating on its carrier so that the so called velocity of the planet gear relative to the carrier is the planet local velocity minus the carrier velocity.

How can one add to different velocities that are at different points in space?
is there a mathematical proof?
 
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