The best way to tell if a rope is static or dynamic is to check the label on the end of the rope. If the label is too worn to read then the only other way is to test the rope.
How To Test If A Rope Is Static Or Dynamic
To check if a rope is static or dynamic the best thing to do is hang it up and give it a pull. If the rope is dynamic you can expect a stretch of around 40% on average. If the rope is static you typically expect to see less than 5% stretch.
Can You Rappel on a Dynamic Rope?
Yes, you can use dynamic ropes to rappel and in certain situations that require a lot of movement, these can be preferable. But be aware your dynamic rope will offer a lot more stretch than a fixed rope so if you need to stay in fixed positions a static rope would be much better.