# Rotational Dynamics (Rotating pulley)

## Homework Statement

The descending pulley shown in the figure has a radius 20 cm and moment of inertia $$0.2 kg m^{2}$$. 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, isnt 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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you should be able to get the mass from the given moment of inertia --- sometimes also known as the "angular mass" or "mass moment of inertia."

Edited to add: Hint: what shape is the pulley?

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you should be able to get the mass from the given moment of inertia --- sometimes also known as the "angular mass" or "mass moment of inertia."

Edited to add: Hint: what shape is the pulley?

It hasnt been provided in th question- the shape of the pulley- Can it be assume to be a disk!

Also I need assistance on this equation of mine!
Do u agree that the 2* acceleration of pulley = acceleration of block(a)

Then while using a=r*$$\alpha$$
what shall I put a?? acceleration of pulley or of block???