1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Work and Mechanical Energy & Moment of Inertia Derivation?

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data

    We did something very similar to this in lab

    http://webenhanced.lbcc.edu/physte/phys2ate/2A LAB HANDOUTS/Moment of Inertia.pdf

    Use Work and Mechanical Energy to derive the expression for the experimentally determined moment of inertia.

    2. Relevant equations
    Wf= work of friction = Delta E = Ef - Ei

    Wf= work of friction = Uf + Kf - Ui - Ki

    U= Potential Energy

    K = Kinetic Energy

    Kf = (1/2)(m + mf)(Vf)^2 + (1/2)(I)(omegaf)^2

    I = Moment of Inertia

    Omegaf = angular acceleration

    Average Velocity = v = (Vf + Vi)/(2)

    If Neccessary

    s=(1/2)*a*t^2

    Torque= F*r= m*r*a

    T= (mf + m)(g - a) = tension

    Ui= mgh

    Uf= mfgh

    K(rotate) = (1/2)(I)(omegaf)^2

    I = Moment of Inertia

    K(linear) = (1/2)(m + mf)(Vf)^2

    Experimentally Moment of Inertia

    I=r^2(m((gt^2/2s)-t) - mf)

    Trying to get to this ^

    mf= mass effective not much meaning just mass in kg
    If it confusing the gt^2 is divided by 2s then it is subtracted by t and multiplied by r^2 and then minus mf


    3. The attempt at a solution

    Wf = work of friction = Uf + Kf - Ui - Ki

    The final potential energy and initial kinetic energy are both zero so this only leaves

    Wf = Kf - Ui

    Wf = ((1/2)(m + mf)(Vf)^2) + (1/2)(I)(omegaf)^2 - mgh

    Wf = (1/2)(m + mf)(s/t)^2 + (1/2)(I)((s/t)*(1/r))^2 - mgh

    Wf = (1/2)(m + mf)(s^2/t^2) + (1/2)(I)((.5*a*t^2)/(t) * (1/r))^2

    Wf = ((1/2)(m + mf)((1/2)*(a*t^4)*(t^2)) + ((1/2)(I)(a*t) * (1/r))^2

    Wf = ((1/8)(m + mf)(a^2 * t^2) + (1/8)(I)((a^2 * t^2)/(r^2))

    Wf = (1/8)(a^2*t^2)((m + mf) + (I/r^2))
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Mar 29, 2009 #2
    So....what is your question?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Work and Mechanical Energy & Moment of Inertia Derivation?
Loading...