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Homework Help: Rotational Motion: Disc Movement

  1. Apr 6, 2009 #1
    1. The problem statement, all variables and given/known data
    A 750 gram grinding wheel 25.0 cm in diameter is in the shape of a uniform solid disc. When it is in use it turns at a constant 220 rpm about an axis perpendicular to its face through its center. When the power is switched off the wheel stops in 45.0 s with constant angular acceleration due to friction

    A) What is rotational intertia of the wheel?
    B) What is the initial angular velocity in rad/s?
    C) What is the constant angular acceleration in rad/s^2?
    D) What is the magnitude of the torque exerted by friction in N-m?

    m = 0.750 kg
    r= 0.125 m
    wf = 23.04 rad/s (converting 220rpm)
    t= 45.0 s

    2. Relevant equations
    Part A) Idisc= 0.5(mr^2) = 0.5(0.750kg)(0.125m^2) = 5.86*10^-2 kgm^2

    3. The attempt at a solution

    I was thinking along these lines... I could find part C first (angular acceleration - alpha) and use that to find part B (initial angular velocity - w0) by using this equation : wf = w0 + alpha(time). I could then find part D (torque - T) by using this equation : alpha = T/I

    My problem is finding angular acceleration, or alpha.

    This is what I did, please let me know if it's correct or not.

    v(speed)= radius*wf
    v = (0.125m)(23.04 rad/s) = 2.88
    vf= v0 +a(linear)(time)
    2.88 = 0 +a(45seconds)
    a(linear) = 0.064 m/s
    a(linear) = radius*a(angular)
    0.064 = 0.125*a
    alpha = 0.512 rad/s^2

    If it's wrong, could you please advise on how to get the right answer?
    Thank you in advance :)

    Disclaimers: This is my first post, so please be gentle! Also, this is not homework, it is a practice test. Thanks again!
    Last edited: Apr 6, 2009
  2. jcsd
  3. Apr 6, 2009 #2
    Did I read this wrong... I assumed wf= 220rpm = 23.04 rad/s. Is the 220rpm actually w0? And if so, am I just converting it wrong?
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