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Angular acceleration in moment of inertia

  1. Dec 15, 2015 #1
    I'm having a hard time undertanding a concept of moment of inertia and Angular acceleration.
    1. The problem statement, all variables and given/known data
    Capture.JPG
    We have a closed system above. M1 is a cylinder of 2 Kilograms, moment of inertia of a cylinder ( MR2 /2 ) with a string tightly rolled around it. This string connects to a free hanging mass (m kilograms) from a ideal massless pulley like in the picture. Gravity is present but has uknown value. The surface under M1 has a static friction coefficient of .1 . When the System is released from Rest the mass descends. The Radius of the cylinder (R) is unknown.

    Determine the maximum value of m so that the cylinder rolls without sliding

    2. Relevant equations
    Sum of Moment of inertias on Cylinder = MR2 /2 . α
    α.R=a
    F=ma
    μE =.1
    3. The attempt at a solution
    let a be acceleration of the string (mass m) and acm be the acceleration of M's center of mass. Ψ will be the force of friction.
    mg-T=ma
    m= T/(g-a)
    T+Ψ=Macm (Ψ and T vectors have same direction.

    My problem with this case stems from the moment of inertia equation.
    We have the following:
    TR -ΨR=(MR2 /2)α

    Simplifying we get 2T -2Ψ=MRα
    In the solution given to us by the teacher, multiplying the angular acceleration by the radius would give us the acceleration of the center of mass of the cylinder. I feel something is wrong since usually the equation gives the acceleration for the edge of the cylinder which is not the same as the center.
     
  2. jcsd
  3. Dec 15, 2015 #2

    haruspex

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    It's not a closed system. The frictional force is external, as are the forces on the string from the pulley, but they don't affect your attempted solution.
    That would be the acceleration of a perimeter point relative to the centre. Here your teacher is simply reversing that, using it for the acceleration of the centre relative to the edge.
     
  4. Dec 15, 2015 #3
    Excuse me?
     
  5. Dec 15, 2015 #4
    While explaining my reasoning in an upcoming reply I found what I was doing wrong.
     
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