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?
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
answer
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