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2 Questions for the price of 1

  1. May 13, 2010 #1
    Oscillation and Rotation

    1. The problem statement, all variables and given/known data

    Question nr 1:

    You have ruler of length L and thickness 2d resting, in equilibrium , on a cylindrical body of radius r. Slightly unbalancing the ruler, and existing attrition between the surfaces prove that the ruler has a oscillatory motion of period:
    [tex] T = 2\cdot \pi\cdot \sqrt{\frac{L^2}{12\cdot g\cdot (r-d)}} [/tex]

    SemTtulo.jpg

    Question nr 2:

    Assuming the sphere roles down without sliding prove that the acceleration of it's center of mass is:

    [tex] a= \frac{g\cdot \sin(\theta)}{1+\frac{2}{5}\cdot \frac{1}{1-\frac{1}{4}\cdot \alpha^2}}[/tex]

    Where g is the gravitational acceleration and
    [tex]\alpha= \frac{L}{R}[/tex]

    Note: The moment of inertia of the sphere is:
    [tex]I= \frac{2}{5}\cdot M\cdot R[/tex]

    SemTtulo-1.jpg

    2. Relevant equations

    [tex]T=\frac{2\cdot \pi}{\omega}[/tex]

    [tex]\tau= F\cdot r\cdot \sin(\varphi)[/tex]

    3. The attempt at a solution

    At question nr 1 I can't wrap my mind about the idea that the ruler won't immediately begin to fall and in question nr 2 I get to:
    [tex]a= \frac{g\cdot \sin(\theta)}{1+\frac{2}{5}\cdot \sqrt{\frac{1}{1-\frac{1}{4}\cdot \alpha^2}}}[/tex]
     
    Last edited: May 14, 2010
  2. jcsd
  3. Mar 25, 2012 #2
    Re: "2 Questions for the price of 1"

    moment of inertia of sphere is I=(2/5).M.R^2
     
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