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World Transform is like a set of Transform properties for the Particular system as a whole. These parameters let you changes the position and rotation of the whole particle system. World Transform changes the camera perspective without moving the camera in the scene. In other words, you don't have to move the After Effects camera to move the particles, which frees you to do a lot of interesting animation.
World Transform may not be compatible with Physics> Bounce mode. The reason is difficult to explain. Basically it would be compatible with an infinite floor rotated in Y only, but any other change (position or rotation) will break the bouncing off of After Effects' layers. Or the layers would have to be moved/rotated exactly the same way as in World Transform.
X, Y, Z Rotation W
The Rotation W parameters set the movement of the rotation of the entire particle system.
X Rotation W rotates the system around a horizontal X-axis. Lower values rotate away from the camera. Higher values rotate toward the camera.
Y Rotation W rotates the system around a vertical Y-axis. Lower values rotate towards the left. Higher values rotate toward the right.
Z Rotation W rotates the system around the Z-axis. Lower values tilt towards the left. Higher values tilt toward the right.
X, Y, Z Offset W
The Offset W parameters set the movement of the position of the entire particle system.
Left to right: X Offset W at -120, 0, 120.
Left to right: Y Offset W at -150, 0, 150.
Left to right: Z Offset W at -200, 0, 200.