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Parallel Axis Thereom to find angular velocity

  1. Jul 21, 2011 #1
    1. The problem statement, all variables and given/known data
    A meter stick is freely pivoted about a horizontal axis at the 94.7 cm mark. Find the (angular) frequency of small oscillations, in rad/s


    2. Relevant equations
    I=Icm+md^2
    [itex]\Sigma[/itex] [itex]\tau[/itex]=I [itex]\alpha[/itex]
    mg*sin([itex]\Theta[/itex])=-I(d^2[itex]\Theta[/itex]/dt^2)
    3. The attempt at a solution
    5.37 rad/s
     
  2. jcsd
  3. Jul 24, 2011 #2
    Hi,

    The torque equation you wrote should be: -mgd*sin[itex]\theta[/itex]=Id^2[itex]\theta[/itex]/dt^2
    (you forgot the 'd' on the left-side.)

    For small angles, sin[itex]\theta[/itex][itex]\approx[/itex][itex]\theta[/itex]

    The torque equation can then be rewritten as:

    -(mgd*[itex]\theta[/itex])/I=d^2[itex]\theta[/itex]/dt^2

    This is a common differential equation that arises in physics, and it describes a type of oscillatory motion known as "simple harmonic motion".

    The period is:

    T=2[itex]\pi[/itex]*[itex]\sqrt{I/mgd}[/itex]

    The angular frequency can be easily found from here.
     
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