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Homework Help: Centripetal and Tangential Acceleration of drill bit

  1. Mar 8, 2009 #1
    1. The problem statement, all variables and given/known data
    An electric drill bit starts from rest and rotates with a constant angular acceleration. After the drill has rotated through a certain angle, the magnitude of the centripetal acceleration is twice the magnitude of the tangential acceleration. What is the angle?


    2. Relevant equations
    ac=rw2
    aT=r.angular acc
    angular acc=(w-w0)/t-t0
    w=angular displacement/t

    3. The attempt at a solution
    ac=2at
    Therefore
    rw2=2r.angular acc
    The radius cancels and therefore
    w2=2angular acc
    =2(w-w0)/t
    Given that the drill bit starts from rest, w0=0 and therefore
    w2=2w/t
    Divide throughout by w and we have
    w=2/t
    Sub w=angular displacment/t and we have
    angular displacement/t=2/t
    t cancels and we are left with
    angular displacement=2 rads
    This is not the answer given in the textbook, the answer is 1 rad
    Please advise where I'm going wrong
     
  2. jcsd
  3. Mar 8, 2009 #2

    LowlyPion

    User Avatar
    Homework Helper

    Consider that ω2r is your Centripetal acceleration.

    And that your Tangential acceleration is a = α*r.

    You know from kinematics that ωf2 = ωi2 + 2*α*θ or since there is no initial ω :

    ω2 = 2*α*θ

    So ... for the given that

    ω2*r = 2*α*r

    Substitute for ω2
     
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