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Angular Acceleration of a grinding wheel

  1. Nov 25, 2008 #1
    1. The problem statement, all variables and given/known data
    A vertical grinding wheel is a uniform disk of mass 62 kg and radius 45 cm. It has a handle of radius 69 cm of negligible mass. A 25-kg load is attached to the handle when it is in the horizontal position.
    (a) Neglecting friction, find the initial angular acceleration of the wheel in rad/s^2.
    (b) Find the maximum angular velocity of the wheel in rad/s.

    2. Relevant equations
    I = 1/2MR^2 + mr^2
    t = mgr for torque
    a = t/I for angular acceleration
    mgr = 1/2Iw^2
    3. The attempt at a solution

    a) Neglecting friction, find the initial angular acceleration of the wheel.
    9.31 rad/s^2
    I found I which is 18.18 kg m^2 using the above equation.
    I then gound T(t) which is 169.23 Nm
    a = t/I = 9.31 rad/s^2

    (b) Find the maximum angular velocity of the wheel.
    I used mgr = 0.5Iw^2 and got w = 3.32 rad/s

    ***What am I doing wrong?? I know both are wrong answers. I think I am doing something wrong for part a. Please help!!
    Thanks
     
  2. jcsd
  3. Nov 25, 2008 #2

    LowlyPion

    User Avatar
    Homework Helper

    Welcome to PF.

    I think for a) your method is OK. I calculate 9.2 m/s2
    with I = 18.38 but let's not quibble too much over that.

    For b) though I think you are overlooking that the 25 kg weight has dropped .69 m and not the r of .45.
     
  4. Nov 25, 2008 #3
    I understand it now....Thanks.
     
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