# Pulleys pulleys everywhere!

A reel has a hub radius $$R$$, the peripheral radius $$3R$$ and mass $$4m$$. Its moment of inertia about its axis is $$3 m R^2$$.

A thin massless thread is wound on a reel. A block of mass $$m$$ is hung through massless and frictionless pulleys as shown.

The reel is placed on a rough horizontal surface where the friction is sufficient to prevent slipping. The system is released from rest. Find acceleration to 2 decimal places (in $$\text{cm/s}^2$$) of the center of mass of the reel. Take $$g= \SI{10}{\meter\per\second\squared}.$$

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