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Rotational question

  1. Apr 21, 2014 #1
    1. The problem statement, all variables and given/known data
    The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:
    A) the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 4
    B) the magnitues of the angular velocity is multuplied by a factor of 4 and the angular acceleration is not changed
    C) the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 2
    D) the magnitues of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed
    E) the magnitues of the angular velocity is multiplied by a factor of 2 and the magnitudeof the angular acceleration is multiplied by a factor of 4

    answer is E

    2. Relevant equations



    3. The attempt at a solution

    Okay i tried working back from this and must be doing something wrong,

    I start with Aradial = v^2/r = rω^2
    and Atangential = rα

    I rearange for A = Aradial + Atangentail (as vectors)

    which is = r√α^2 + ω^4

    subbing in 4 and 2 i get r√32
     
  2. jcsd
  3. Apr 21, 2014 #2

    Simon Bridge

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    You have interpreted "acceleration" in the question to mean the total acceleration.
    For circular motion, radial acceleration (##\small{\ddot r}##) is zero - so you are summing the tangential and centripetal acceleration.

    So ##a=r\sqrt{\omega^4+\alpha^2}##

    So far so good - but
    ...what did you put 4 nd 2 into and why?

    Consider, multiplying angular velocity by 2 means that where you see a ##\omega## before, you put a ##2\omega##.

    Working in reverse is a good idea.
    You need to put ##a_{new}=4a=4r\sqrt{\omega^4+\alpha^2}##... work out how that 4 fits against the angular terms.
     
  4. Apr 21, 2014 #3
    |a| = r√(α24) ,Now when you put αnew=4α and ωnew =2ω ,you get r√(16(α24)) = 4r√(α24)

    Hence option E is correct.
     
  5. Apr 21, 2014 #4
    ohhh of course.. thanks
     
  6. Apr 21, 2014 #5
    I think your mistake is that you are substituting values when you should be substituting in ratios.
     
  7. Apr 21, 2014 #6

    rude man

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    FINAL (I hope) EDIT:

    I agree it's E.
     
    Last edited: Apr 21, 2014
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