A tightrope walker remains standing by keeping his center of mass directly above the rope. If his center of mass moves off center, he must correct this or he will rotate off the rope and fall down. By carrying a long pole, the performer is increasing his rotational inertia. This means that he will rotate slower and therefore have more time to make a correction to his center of mass. The balancing poles are frequently droopy and weighted at the tips. This lowers the center of mass of the performer, which also makes it easier to balance.
That's what my mom thought but I didn't really get how it worked. In fact, I still don't know how the whole "rotational inertia" thing works but I just get that it helps give you more time to shift your center of mass if you get off balance. :D
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