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Homework Help: Moment of Inertia

  1. Dec 15, 2009 #1
    Here is the problem I am working on. Here is the work I have so far, does this look right.
    A grinding wheel that has a mass of 65.0 kg and a radius of 0.500 m is rotating at 75.0 rad/s. (The carousel can be modeled as a disk and assume it rotates without friction on its axis)

    a) What is the moment of inertia of the grinding wheel?

    I=MR^2. So I=(65kg)(.5m^2)=16.25 kgm^2



    b) A brake is applied to the outer edge with a force of 45 N. What is the resulting torque?

    Torque=r*f. So (.5m)(45N)=22.5 Nm



    c) What is the resulting angular acceleration of the grinding wheel?
    Fr=mra. So 22.5=(65kg)(.5)(a). a=.69 m/s^2.





    d) How much time passes until the wheel comes to a stop?

    not sure what to do here. I know that its rotating at 75r/s. And a 45N brake is being applied. I dont know what relates time to radians and force.




    e) How many revolutions does the wheel go through as it comes to a stop?


    This can be determined by dividing the answer from d by its velocity.

    any help will be greatly appreciated!!
     
  2. jcsd
  3. Dec 15, 2009 #2

    rock.freak667

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    Homework Helper

    You can assume the angular acceleration is constant, so you can use the equations of rotational motions

    [tex]\omega= \omega_0 + \alpha t[/tex]
    [tex]\omega^2=\omega_0^2+2 \alpha \theta[/tex]
    [tex]\theta=\omega_0 t +\frac{1}{2}\alpha t^2[/tex]
     
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