Acceleration of a cotton reel

Two forces of 100N100N and 20N20N act on a cotton reel of inner radius 5 m5 \text{ m} and outer radius 10 m10 \text{ m} as shown in the figure above. The reel is performing pure rolling motion. The surface produces sufficient necessary friction for pure rolling of the reel. Find the linear acceleration of the reel (in  m/s2\text{ m/s}^2).

Details and Assumptions

  • The mass of the cotton reel is 10 kg10 \text{ kg}.

  • The moment of inertia of the reel about central axis is 1000 kg m21000 \text{ kg m}^2.

The problem is original.

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