Hula-Hoop Madness!

March 1, 2021
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First marketed by Wham-O in 1958, the Hula-Hoop was not patented until March of 1963. In the first four months of production, it is estimated that 25 million Hula-Hoops were sold. According to the Guinness Book of World Records, the record for the most Hula-Hoops twirled simultaneously by an individual, set in November of 2015, is 200. This record was set by Marawa Ibrahim. Another Hula-Hooper, Gregory Sean Dillon, is the fastest Hula-Hooper in the world, twirling at a rate of 243 revolutions per minute.

At the circus, a performer twirls a Hula-Hoop around her arm. Assume the Hula-Hoop has a radius of 18 inches, and the performer’s arm is completely round with a diameter of 4 ½ inches. If point A of the Hula-Hoop is currently touching the performer’s arm, after how many revolutions around her arm will point A first be on the performer’s arm again? 


What fraction of the Hula-Hoop’s circumference makes contact with the performer’s arm during one successful revolution of the Hula-Hoop around her arm? Express your answer as a common fraction.


During her act the performer twirls the Hula-Hoop without ceasing for 6 minutes at a rate of 2.5 revolutions per second. If she starts her act with point A of the Hula-Hoop touching her arm, how many times does point A again touch her arm during her 6-minute performance?