(This is one of those duh moments, the ones where I say to myself: "Man, that is so simple how could I have missed it?")
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In Austin, there is frisbee golf, ultimate frisbee, and I wouldn't be surprised if a food stand serves their fare on a frisbee. Austin is a great place for frisbee fun, just as much as it is a town of guitar enjoyment. Fortunately, there's a strong correlation between throwing a frisbee and strumming an acoustic guitar.
Everyone plays guitar in their own way, but it is difficult to play fast strums with a wrist that doesn't move. It's harder on the arm because more muscles are engaged including ones that do not need to be. Tension will quickly enter the arm, resulting in either a forced tone or muscle fatigue. No bueno in either case! However, the whip of the wrist a person needs to throw a frisbee and the rhythmic strums on an acoustic guitar are very similar to each other. Inertia is the key. When a person's wrist doesn't move, it's difficult to allow the whip of the wrist to fly upwards in an upstroke, and fall downwards on a downstroke. When it's looser, the arm moves less.
Now comes the advice: Whip the strumming hand like you would a frisbee when strumming. If that hurts your wrist, don't do it. Ignore! For most people this will feel awkward at first, but it has the potential for making a particularly difficult strumming rhythm a whole lot easier.