1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Torque and Rotational Kinematics

  1. Nov 3, 2007 #1
    1. The problem statement, all variables and given/known data
    A grindstone in the shape of a solid disk with diameter 0.490 m and a mass of m = 50.0 kg is rotating at omega = 890 rev/min. You press an ax against the rim with a normal force of F = 170 N, and the grindstone comes to rest in 7.20 s.

    2. Relevant equations

    τ=Iα
    ωz0zkαt
    τ=r×F

    3. The attempt at a solution
    [tex]\tau =I\alpha[/tex]

    [tex]{\omega }_z={\omega }_{0z}+{\mu }_k\alpha t[/tex]

    [tex]I=\frac{1}{2}MR^2[/tex]

    [tex]\tau =\frac{1}{2}MR^2\alpha[/tex]

    [tex]{\omega }_z=0\alpha =\ \frac{{\omega }_{0z}}{{\mu }_kt}[/tex]

    [tex]\tau =-\frac{1}{2}Mr^2\frac{{\omega }_{0z}}{{\mu }_kt} [/tex]

    [tex]\tau =r\times F[/tex]

    [tex]r\times F=\frac{1}{2}Mr^2\frac{{\omega }_{0z}}{{\mu }_kt}[/tex]

    [tex]{\mu }_k=\frac{Mr{\omega }_{0z}}{2tF}[/tex]

    [tex]F=f{\mu }_k[/tex]

    [tex]{\mu }_k=\frac{Mr{\omega }_{0z}}{2tf{\mu }_k}[/tex]

    [tex]{\mu }^2_k=\frac{Mr{\omega }_{0z}}{2tf}[/tex]

    [tex]{\mu }_k=\sqrt{\frac{Mr{\omega }_{0z}}{2tf}} [/tex]
     
    Last edited: Nov 3, 2007
  2. jcsd
  3. Nov 3, 2007 #2
    Okay, although not provided in the question, I am assuming that you are supposed to find coefficient of kintic friction. (Your attempt at the solution tells me that.)
    You erred in this statement:
    Note that, torque produced by F is not the one which is producing deceleration in the disc (It is in a perpendicular direction to ωz!), rather it is f, torque due to friction which is producing deceleration. Keep this in mind and I hope you would be able to solve it, as you know other things, it seems.
     
  4. Nov 6, 2007 #3
    [tex]F=f{\mu }_k[/tex] <---isn't that the force due to friction? Or am I confused? Realizing I kind of messed up my notation, [tex]f = 170N[/tex] and [tex]F_{friction}=F[/tex]
     
    Last edited: Nov 6, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Torque and Rotational Kinematics
  1. Rotational Kinematics (Replies: 2)

Loading...