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Potential Energy - Energy Considerations to Derive Simple Harmonic Motion

  • 06-06-2009 10:15am
    #1
    nitrogen
    Closed Accounts Posts: 698 ✭✭✭


    Hello,

    I have a query regarding an experiment at the end of this physics lecture (Last 10 minutes) about potential energy and Simple Harmonic Motion.



    Problem
    The known radius of a circular air track is used to predict the period of oscillation of a sliding object (small angles!), and a measurement is made to confirm this. The process is repeated for a ball bearing rolling in another circular track. The period of oscillation can now not be predicted in a similar way as was possible in the case of the air track. Why? ==> No, it has nothing to do with friction!

    My theory is some of the potential energy is converted into kinetic energy in rotating the ball bearing. Thus the prediction from the equation is off. If someone has the interest and time, could anyone explain if I am right or wrong and maybe elaborate a little?

    Thanks.

    ps. These lectures are fantastic for anyone intrigued by Prof. Walter Lewin, and can be downloaded directly from MIT's site or found in iTunes.


Comments

  • #2
    ZorbaTehZ
    Registered Users, Registered Users 2 Posts: 2,149 ✭✭✭ZorbaTehZ


    Ye, it's because it is rotating, whereas in the first case total energy U = 1/2 mv^2 + mgh (kinetic + potential) you now have the rotational energy 1/2 Iω^2 to consider.

    Although I would argue that it is incorrect to say that it is conversion from potential to kinetic, rather kinetic to rotational since if the period is longer then kinetic must be lower and since potential should remain unchanged relative to the first experiment (it's vertical position is unchanged), it must be reduced kinetic.

    EDIT: When I say kinetic to rotational, I mean "normal"or forward kinetic to rotational kinetic in case of confusion.


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