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Given initial angular velocity of wheel, find revolutions to rest

  1. Jun 8, 2009 #1
    SOLVED Given initial angular velocity of wheel, find revolutions to rest

    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 [tex]\vartheta[/tex] / dt = 4.1e-.088335775t
    where the initial angular velocity is 4.1 rad/s.
    Find the number of revolutions it makes before coming to rest.



    2. Relevant equations
    d [tex]\vartheta[/tex] / dt = 4.1 rad/s-.088335775t


    3. The attempt at a solution
    To find the time needed for the wheel to rest, I set the left side of the equation to 0, but to find t, I had to find the natural log of both sides. However, ln of 0 does not exist...so now I am at a loss. Any help would be appreciated...thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Jun 8, 2009
  2. jcsd
  3. Jun 8, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    First of find the angular acceleration by taking he derivation of angular velocity.
    α =kω, where k = -0.08833577.
    Then use the equation θ =Intg [( ω^2 - ωο^2)/2α]*dω between the limits ωο to 0, find the total angular displacement. From that you can find the number of rotations.
     
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