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
    [itex]\Sigma[/itex] [itex]\tau[/itex]=I [itex]\alpha[/itex]
    3. The attempt at a solution
    5.37 rad/s
  2. jcsd
  3. Jul 24, 2011 #2

    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:


    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:


    The angular frequency can be easily found from here.
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