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Integration of an energy balance equation, with respect to time.

  1. Aug 29, 2011 #1
    Hi Guys, I was hoping someone would be able to help me with this integration. It's been killing me haha.

    I've got this energy balance equation:

    mgh = 0.5m(v^2) + 0.5I(w^2) + T(theta)

    Basically, It's a gravitational potential energy that is converted to a velocity of a falling object, a rotating flywheel and some frictional Torque (T). v is velocity, and w is angular velocity. I is the moment of inertia, which is known.

    I need to integrate this expression with respect to time, t. I can relate velocity to angular velocity by: 0.0395w. I also thought I could express theta as angular velocity multiplied by time.

    Any help would be greatly appreciated as I cannot get this out at all.
  2. jcsd
  3. Aug 30, 2011 #2


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    welcome to pf!

    hi lukea125! welcome to pf! :smile:

    (have a theta: θ and an omega: ω :wink:)
    no :redface:

    you have (dθ/dt)2 as a function of θ …

    so square-root it, separate the variables, and integrate :wink:
  4. Aug 30, 2011 #3
    Thanks Tiny-Tim! I really appreciate it. I'll give it a go and see what I can get.
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