Question
Although many orchestra conductors conduct with their bare hands, most use a baton for conducting. We shall take a baton whose shaft is made from
Although many orchestra conductors conduct with their bare hands, most use a baton for conducting. We shall take a baton whose shaft is made from Fiberglass and whose handle is made from Pine. Although typically a baton will not have a uniform mass distribution along its length, we will take this baton to have a uniform mass distribution and calculate the moment of inertia assuming a pivot point at the index finger of the conductor. Each time the conductor "hits" a beat, they indicate this beat using a sudden acceleration of the baton with magnitude 1.8 meters/second2. In order to hold tight onto the baton of mass M and length L, the conductor applies equal and opposite normal forces from their index finger and thumb of magnitude 35 Newtons. These forces are applied to the point such that the short side of the baton is 23 percent of the total length. Conducting is quite a workout and the conductor is running a mild fever of 101 degrees Fahrenheit, and the resulting sweat lowers the coefficient of static friction between the fingers and the baton to 0.07. The drag coefficient in air should be taken to be 0.0021.
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