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Torque required to decelarate a disc

  1. Oct 8, 2015 #1
    Hello everyone if someone can helo me out here
    I have a rotating shaft wiht a disc mounted on it.The moment of inertia of the total system is 170 kgm2.It is rotating with a veolicty of 20 deg /sec.i want to bring it to stand still within 80 deg travel from the application of brakes

    I=170 kgm2
    wi=20 deg/sec=0.34 rad/sec
    wf=0
    Δt=4 sec(taken from the fact that it is moving at speed of 20 deg/sec,80 deg/sec will be covered in 4 sec.Please correct as i m not sure abt this value)

    So
    T=Iα
    T=I(Δω/Δt)
    T=(170) (0-0.34/4)
    T= -14.45Nm

    Please correct and help
     
  2. jcsd
  3. Oct 8, 2015 #2
    You cannot simply set it as 4 seconds because when it slow down, the disc stop before it rotate 80 deg after the application of brakes.

    Just leave it as variable and consider
    [tex] T = \dfrac{d\omega}{dt} = \dfrac{d\theta}{dt} \dfrac{d\omega}{d\theta} = \omega \dfrac{d\omega}{d\theta}. [/tex]
    When you integrate it as [itex] \theta[/itex], then
    [tex] \int_{\theta_i}^{\theta^f} T d\theta = T(\theta_f - \theta_i) [/tex]
    and also it is same as
    [tex] \int_{\theta_i}^{\theta^f} T d\theta = \int_{\omega_i}^{\omega_f} \omega d\omega = \dfrac{1}{2} \left(\omega_f^2 - \omega_i^2\right). [/tex]
     
  4. Oct 8, 2015 #3
    hey thnks for the reply.....can you elaborate it more....possibly solve it
     
  5. Oct 8, 2015 #4
    Use the last relation,
    [tex] T(\theta_f - \theta_i) = \dfrac{1}{2} (\omega_f^2-\omega_i^2), [/tex]
    for your situation. You already know each variable without [itex] T [/itex], so it is elementary calculation
     
  6. Oct 8, 2015 #5
    ok thnks....but cant i determine a stopping distance?
     
  7. Oct 8, 2015 #6
    You mention that you want to stop the disc within 80 deg,
    so just set [itex] \theta_i = 80^\circ [/itex] and [itex] \theta_f = 0 [/itex]. It's up to you.
     
  8. Oct 8, 2015 #7
    And what abt the inertia....i see you have ignored inertia in your equations
     
  9. Oct 8, 2015 #8
    Oh! Sorry. I used [itex] T [/itex] for the angular acceleration. The equation should be
    [tex] \alpha (\theta_f - \theta_i) = \dfrac{1}{2} (\omega_f^2-\omega_i^2), [/tex]
    and then
    [tex] T = I \alpha [/tex].
    It's my mistake.
     
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