This is a typical 'propeller clock' type application. You will need to use something to determine not just the RPM, but also to know when to begin displaying your frame per revolution, or else your graphics would get garbled.

You can easily use IR to generate your index pulse; Mount the continuously lit IR LED on the chassis, and an IR detector on the spinning platform. Align them such that they see each other once every revolution.

Regards,

Anand