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Dynamics of rotational motion: Atwoods machine

Atwoods Machine

Two blocks, A and B are attached to each end of a cord attached to a pulley C. Block A hangs slightly higher than Block B. Find the linear accelerations of block A and B, and the angular acceleration of the wheel C and the tension in each side of the cord if there is no slipping between the cord and the surface of the wheel. The masses of blocks A and B are Ma and Mb, respectively, the moment of inertia of the wheel about its axis is I, and the radius of the semicircle in which the string moves is R.

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See attachment for free body diagram.

let the tension on block A is Ta and B side is Tb. Let linear acceleration is a and angular acceleration is ...

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