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Angular speed question please help.

  1. Mar 21, 2008 #1
    1. The problem statement, all variables and given/known data
    As a result of friction, the angular speed of a wheel changes with time according to
    d θ/d t = ω_0 e^(−σ t) ,
    where ω0 and σ are constants.
    initial angular speed = 5.45 rad/s
    σ =.23913
    Determine the number of revolutions the wheel makes after 2.33 s .
    Answer in units of rev.

    3. The attempt at a solution

    I know I have to take the integral which is:
    θ = - w_0/(σ *e^(-σ *t))
    My numbers are initial velocity= 5.45 rad/sec, sigma= .023913, and time=2.33 seconds. so when I solved I got -13.0589 radians and divided it by 2pi to get revolutions, which gave me -2.07839. I thought the answer would be 2.07839 because revolutions can't be negative but it is not right, should i use the negative or am i doing something wrong?
  2. jcsd
  3. Mar 21, 2008 #2


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    Science Advisor
    Homework Helper

    Hi jj! :smile:

    I'm with you on this: the question is badly worded. :frown:

    The wheel makes 2.07839 revolutions clockwise!

    However, that's clearly not the answer they want - if this is a computer thing where you're only allowed to put in a number, then you must put in the number they want - this isn't a constitutional rights case!

    But if you're allowed a full answer, write something like "-2.07839 revolutions in the direction of increasing θ (2.07839 revolutions in the direction of decreasing θ)" - with the answer they want first. :smile:
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