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## Homework Statement

The descending pulley shown in the figure has a radius 20 cm and moment of inertia [tex]0.2 kg m^{2}[/tex]. The fixed pulley is light and the horizontal plane frictionless.

Find the acceleration of the block if its mass is One kg.

http://img367.imageshack.us/img367/1808/diagrammj2.jpg [Broken]

## The Attempt at a Solution

I am not sure whether the lower pulley will rotate or not but as the moment of inertia and the radius is given, I think it will. Please explain this:

Assuming the lower pulley rotates.

Tension in the left segment =T

And in the right segment =T' (since there must be friction present for the lower pulley to rotate)

T=a (a is acceleration of block)

Mg-(T+T')=Ma*0.5 (where M is the mass of the pulley - which is unknown, how will I take this out?)

The acceleration of the pulley will be half the acceleration of the block, isn't it?

Torque=I*angular acceleration

0.2(T'-T)=0.2(a/2R) (R=0.2 m given)

The answer given in my book is 10 m/s2 but I am not sure how to get the mass of the pulley? Where exactly am I going wrong?

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