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!

Homework Help: Calculating moment of inertia about a door hinge.à

  1. Dec 4, 2011 #1
    The problem statement, all variables and given/known data
    A solid door of mass 39.30 kg is 2.34 m high, 1.68 m wide, and 3.23 cm thick.

    What is the moment of inertia of the door about the axis through its hinges?

    If the edge of the door has a tangential speed of 76.5 cm/s, what is the rotational kinetic energy of the door?

    The attempt at a solution

    I don't really know where to start. Should I find the center of mass of the door? Because I = Ʃmr^2?

    I know how to solve for the second half (Ek = (1/2)Iω^2), but I'm not sure how to calculate I.
  2. jcsd
  3. Dec 4, 2011 #2
    The moment of inertia of a thin rod of mass m and lenght L about an axis at one of its ends and perpendicular to the rod is given by
    I = [itex]\frac{mL^{2}}{3}[/itex]

    Now let us imagine the door to be a set of thin rods parallel to the axis passing through the hinges.
  4. Dec 4, 2011 #3
    I have the answer to the first question, but I'm not nearly as well off with the second question as I had assumed.

    I got 37 kgm^2 for the first question.

    I assumed you would take that value and take 76.5 cm/s (.765 m/s) as ω and plug it into
    E = (1/2)Iω^2

    I get 10.8 when I do that (I used m/s and I'm assuming the units are joules), but that's incorrect.

    Any advice?
  5. Dec 4, 2011 #4
    [itex]\omega[/itex] is the ANGULAR speed i.e. measured in ANGLE per second i.e. rad/s and so you have the convert the TANGENTIAL speed given to ANGULAR speed.
  6. Dec 4, 2011 #5
    Oh! Okay. How do I calculate angular speed from tangential speed?
  7. Dec 4, 2011 #6
    angle (in radians) rotated = distance along the arc / radius
    therefore distance along arc = radius x angle
    i.e. distance along arc/time = radius x (angle /time)
    v = r x w
    v in m/s because linear or tangential
    w in rad/s because angular
  8. Dec 4, 2011 #7
    So to get velocity, I take the linear velocity and multiply it by the width of the door to get ω, and then plug that value into the energy equation?

    Edit: when I do that I get 30.6 J and that is incorrect.
  9. Dec 4, 2011 #8
    v = R[itex]\omega[/itex]
    therefore .... = [itex]\omega[/itex]
  10. Dec 4, 2011 #9
    Got it! Thanks!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook