The strobing effect you describe happens quite readily with fast-moving objects and short or instantaneous “shutter speeds”. As @Box suggests, the easiest approach to lessen the stroboscopic effect is to fudge some aspect of the motion. Reduced rotation rate (as opposed to translation rate) is probably easiest to implement without losing the intended pace of the animation.
I put a lot of effort into minimizing the stroboscopic effect in a video I created with SketchUp a couple of years ago. I wanted to show some high-speed oscillation at real-time rate (using motion-blur to defeat strobing), and in slow motion (naturally no strobing). See the following topic for an explanation and video sample.