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Angular velocity and acceleration

  1. May 25, 2016 #1
    1. The problem statement, all variables and given/known data
    Small mass sits on a circular revolving table, 200 mm from center. It is given a constant angular acceleration of 2 rad/s. The static coefficient of friction is 0.2. At what angular velocity will the mass start to slip?
    pv4ATHI.png

    2. Relevant equations
    ar=v2/r
    ar=r''-rθ'2
    aθ=rθ''+2r'θ'
    ΣFi=mai
    Ff,max=μN

    3. The attempt at a solution
    I first set up a free body diagram with wmass pointing downwards, Ff pointing left, normal pointing upwards, with ar vector pointing to the right.

    Since the distance is unchanging, r = 0.2m, r'=0, r''=0. θ''=2rad/s, θ'=2t rad/s + c, θ=t2+ct+d

    ΣFz=maz=N-mg, since az=0, N=mg
    ΣFr=mar=m(r''-rθ'2)=-Ff
    Combining: m(r''-rθ'2)=-μmg
    Simplifying: -rθ'2=-μg

    θ' = ω = √(μg/r)
    θ' = √(0.2⋅(9.81m/s2)/0.2m) = 3.13 rad/s

    Does this look correct? I never used the given angular acceleration so I feel like I missed something. Thank you.
     
  2. jcsd
  3. May 25, 2016 #2
    That seems right to me. although the acceleration is to the left (which the math seems to identify with already)
     
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