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A uniform disk turns at 2.7 rev/s around a frictionless central axis. A nonrotating rod, of the same mass as the disk a...

A uniform disk turns at 2.7 rev/s around a frictionless central axis. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk(Figure 1) . They then turn around the spindle with their centers superposed.
What is the angular frequency in rev/s of the combination?

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using law of conservation of angular momentum

Idisk * wdisk = (Idisk + Irod) * wf

wf = Idisk * wdisk / (Idisk + Irod)

we know that

Idisk = m*r^2 / 2

Irod = m*L^2 / 12 = m*4r^2 / 12

wf = (wdisk * m*r^2/2) / m*r^2/2 + m*4r^2/12

wf = (wdisk / 2) / (1/2 + 1/3)

wf = o.60 * wdisk

wf = 0.60 * 2.7

wf = 1.62 rev/s

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