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I tried to rotate an object around its z-axis, by using a motion actuator with z-rotation (blue axis in screen) but it rotates around the y-axis (green).

Are y and z-axis for some reasons swaped in the BGE?

enter image description here

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No - Suzanne (the monkey) has her Z axis pointing out from her face, and the Motion actuator defaults to use local coordinates. Either:

  • Apply rotation to the mesh (Object>Apply>Rotation), or
  • Switch the actuator to world coordinates (press the L toggle button on the right of the Rot row).
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