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Easiest Cylinder to Balance - angular acceleration

  1. Mar 25, 2008 #1
    1. The problem statement, all variables and given/known data
    24. A person tries to balance vertically each of three long uniform cylinders with equal radii on the end of his finger:


    * A wood cylinder of mass m and length L with moment of inertia I
    * A bamboo cylinder of mass m and length 3L with moment of inertia 9I
    * A concrete cylinder of mass 4m and length 2L with moment of inertia 16I


    Which object is the easiest to balance and why?

    A. The wood cylinder is easiest to balance because it has the smallest moment of inertia.
    B. The concrete cylinder is easiest to balance because it has the largest moment of inertia.
    C. The concrete cylinder is easiest to balance because it is the most massive.
    D. The bamboo cylinder is easiest to balance because it has the least density.
    E. The bamboo cylinder is easiest to balance because it is longest.

    Correct Answer: E

    2. Relevant equations
    net torque = I*alpha

    3. The attempt at a solution
    I don't understand how the answer is E. I thought the object with the largest moment of inertia would have the smallest angular acceleration. It just seems to me that if the cylinder is longer, the gravitational force will act at a further distance from the support point which would only increase the net torque.
     
  2. jcsd
  3. Mar 26, 2008 #2
    It is actually harder to balance small objects (such as pencils) than large objects (such as broom handles). Tall objects have a higher centre of mass. Basically this means that they will begin falling slowly, giving you a little more time to quickly correct your body to keep the object upright.
     
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