(455) HL Galilean transformations [IB Physics HL]

Introduction to Relativity

• Relativity explores the measurements of position and velocity from different reference frames.

• Two reference frames are considered:

  • S: the stationary frame (ground)

  • S': the moving frame (e.g., a train).

Galilean Transformations

• Position Transformation:

  • Formula: ( X' = X - VT )

    • ( X ): Position in the stationary frame (meters).

    • ( X' ): Position in the moving frame (meters).

    • ( V ): Speed of the moving frame with respect to stationary frame (meters/second).

  • Example: A train moving and the measurements done inside it versus outside.

• Speed Transformation:

  • Formula: ( U' = U - V )

    • ( U' ): Speed of an object in the moving frame (meters/second).

    • ( U ): Speed of the object in the stationary frame (meters/second).

  • Scenario: Someone walking inside a moving train.

Example with the Train

• Observer on Ground:

  • Measures the speed of the train ( V = 4 , ext{m/s} ).

  • Ball Rolled in Train:

  • Speed ( U' = 11 , ext{m/s} ).

  • Find the speed as observed from the ground:

    • Use the formula: ( U = U' + V )

    • Calculation: ( U = 11 + 4 = 15 , ext{m/s} ).

Key Takeaways

• Understanding measurements in relativity hinges on knowing who measures what and in which frame.

• The transformations simplify how we view motion in relation to different observers.

• The foundational concepts in relativity start simple and become more complex as scenarios increase.