Question: Note that in the analysis, to get the angular velocity of the disk, you need to multiply the angular velocity of the smart pulley by

Note that in the analysis, to get the angular velocity of the disk, you need to multiply the angular velocity of the smart pulley by the factor

\frac{R_{p}}{R} .

Why is this necessary?

The smart pulley is smaller than the disk so it will rotate at a different speed. This ratio converts the rotation of the pulley into the rotation of the disk.

The pulley and the disk have much different masses. Multiplying by this factor corrects for the difference in mass.

The pulley has a different shape than the disk, so their rotational inertias are different. This factor corrects between the two.

Note that in the analysis, to get the angular

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