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Find the angular speed at t=3 seconds

  1. Dec 24, 2016 #1
    1. The problem statement, all variables and given/known data
    A shaft is turning at 65.0 rad/s at time zero. Thereafter, its angular acceleration is given by α = -10 rad/s 2 - 5t rad/s 3 where t is the elapsed time. (a) Find its angular speed at t = 3.00 s. (b) How far does it turn in the 3.00 s seconds?

    t=3 seconds
    wi= 65.0 rad/s
    α = -10 rad/s 2 - 5t rad/s 3

    2. Relevant equations
    Wf=Wi+αt where α is the angular acceleration

    3. The attempt at a solution
    since α = -10 - 5t (1)
    at t= 3 seconds
    by substitution in (1):
    α= -25 rad/s2

    From Kinematic equation:
    wf=65-25(3)= -10 rad /s

    I found a different answer in the solutions so please tell me why my answer is incorrect.
  2. jcsd
  3. Dec 24, 2016 #2


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    Looks like you tried to solve it by using an equation restricted to constant angular acceleration. Is the angular acceleration constant in this problem? You calculated α at t = 3 s, but that's not the angular acceleration at other instants of time between t = 0 and t = 3 s.
  4. Dec 24, 2016 #3
    Yes it isn't constant. So basically i can't use kinematic equations if the acceleration isn't constant??
  5. Dec 24, 2016 #4


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    Yes. You need to use differential equations w.r.t. time.
  6. Dec 24, 2016 #5
    Alright. Thanks both of you for the help. Appreciated :)
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