1. Not finding help here? Sign up for a free 30min 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!

Centripetal and Tangential Acceleration

  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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Centripetal and Tangential Acceleration
Loading...