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Cylinder pulled by rope on a rough surface

  1. Aug 13, 2015 #1
    1. The problem statement, all variables and given/known data
    A rope is pulled off with a force F from a combined cylinder. the smaller cylinder's radius is r and the big one's is R. the cylinder rotates on a rough surface without sliding. the force makes an angle θ with the horizon.
    What's the acceleration's "a" magnitude and direction.

    2. Relevant equations
    Rigid body: ##M=I\alpha##
    $$I=kMR^2$$

    3. The attempt at a solution
    Torque relative to the contact point, the torque's arm is:
    $$\left( R-\frac{r}{\cos\alpha} \right)\cos\alpha=R\cos\alpha-r$$
    $$M=I\alpha\rightarrow F(R\cos\alpha-r)=kMR^2\cdot \alpha,\; R\alpha=a$$
    $$\Rightarrow a=R\frac{F(R\cos\alpha-r)}{kMR^2}=\frac{F(R\cos\alpha-r)}{kMR}$$
     

    Attached Files:

  2. jcsd
  3. Aug 13, 2015 #2

    ehild

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    Homework Helper
    Gold Member

    The moment of inertia depends on the position of the rotation axis. You have to specify it. Usually I=kMR2 is used with respect to the centre of the rolling body.
     
  4. Aug 14, 2015 #3
    $$a=R\frac{F(R\cos\alpha-r)}{MR^2(1+k)}=\frac{F(R\cos\alpha-r)}{MR(1+k)}$$
     
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