A uniform disk turns at 2.8rev/s around a frictionless spindle. A nonrotating ro

Question

A uniform disk turns at 2.8rev/s around a frictionless spindle. 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 both turn around the spindle with their centers superposed.

Part A

What is the angular frequency in rev/s of the combination?

Express your answer using two significant figures.

A uniform disk turns at 2.8rev/s around a frictionless spindle. 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 both turn around the spindle with their centers superposed. Part A What is the angular frequency in rev/s of the combination? Express your answer using two significant figures.

Explanation / Answer

The disk has

Idisk = 1/2 mr^2

and the rod has

Irod = 1/3 mr^2

Thus, their total momentum after,

If = 5/6 mr^2

By conservation of momentum,

Ii wi = If wf

--> wf = Ii wi / If

Thus, plugging in Ii = Idisk, If = 5/6mr^2,

wf = 1.7 rev/s [ANSWER]

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