I made a model of a projector, where the projection part is done with a spotlight with material like below.
Now when I move the spotlight away at a high speed, I'd expect some form of motion blur on the projector screen but the image is sharp as if the projector was stationary.
Just to convince myself that motion blur in the scene works at all I've added a light-emitting ball that moves in front of the screen at a rate similar to the spotlight.
Without motion blur
With motion blur (note blurry ball but sharp image)
How can I make a projector that responds to motion blur?