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: Angular Momentum - Train Placed on a Wheel

  1. May 11, 2010 #1
    I've been trying this problem for a while now and can't seem to get the given answer. I know I'm probably making an elementary mistake somewhere but I can't find it.

    1. The problem statement, all variables and given/known data
    A track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis. A toy train of mass m is placed on the track and, with the system initially at rest, the train's electrical power is turned on. The train reaches a steady speed of 0.176 m/s with respect to the track. What is the angular speed of the wheel if its mass is 1.97m and its radius is 0.584 m? (Treat the wheel as a hoop, and neglect the mass of the spokes and hub.) (Answer 0.101 rad/s)

    Ok so:
    Vt= .176 m/s
    mt= M
    m2= 1.97M
    r= 0.584m
    Xf= ?
    (X is angular velocity, subscript t for train and 2 for wheel)

    2. Relevant equations


    3. The attempt at a solution

    So I set it up with the initial equation
    Lt = -L2
    rmtvt = IX

    Then expanded and substituted for corresponding masses
    rMv = 1.97Mr2X

    M cancels and so does an r, so
    vt = 1.97rX

    Then substitute the values
    .176 = 1.97(.584)(X)

    I get a final answer of
    X = .153 rad/s

    The answer is supposed to be .101 rad/s which I can't seem to get.

    Also I used X for angular speed instead of omega because the text formatting wasn't working, and about 4 different symbols showed up instead of omega. Not sure why.
    Last edited: May 11, 2010
  2. jcsd
  3. May 11, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Crusher8576! Welcome to PF! :smile:

    (have an omega: ω :wink:)
    hmm … I got the same answer as you until I read the question more carefully. :redface:

    To find L, you need the actual speed of the train, which isn't 0.176, is it? :smile:
  4. May 11, 2010 #3
    Aha I've got it. Thanks for the help.

    If anyone was wondering how to do it:

    The wheel is spinning in the opposite direction of the train, so the train may have a speed of .176, but that's in relation to the track. I had to find the actual speed of the train in relation to the ground.

    So in the part where I have vt = 1.97rX, replace the Vt with what I called Va (for V actual), and also created Vw for (V wheel).

    And Va = Vt - Vw = Vt - Xr

    So then we're left with Vt - Xr = 1.97rX to solve for X.
    Last edited: May 11, 2010
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook