Acrylic plastic is something you probably know by another name: Plexiglas. This material has a wide range of uses, from the lowly fish tank to skylights. What makes it attractive to builders is that it is lighter than glass and yet weather- and impact-resistant. When it needs to be polished, a careful buffing will restore its clarity.
Turn on the buffing wheel and apply tallow to it. This will help the buffing compound adhere better.
Apply buffing compound to the wheel. Hold the wheel steady as you hold the acrylic plastic with the other hand and move it across the wheel with a back and forth motion. Be careful not to apply excess pressure, as this could mar the acrylic plastic rather than polish it. Keep the acrylic plastic in motion, too, as failure to do so could mar it still further and build up too much heat.
Polish the edges of the acrylic plastic in a similar fashion. However, you need to take extra care not to let the buffing wheel jerk out of your hand.