What is the angular frequency in rev/s of the combination? A uniform disk turns at 2.4 rev/s around a frictionless sp...

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

A uniform disk turns at 2.4 rev/s around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disks diameter, is dropped onto the freely spinning disk(Figure 1). They then both turn around the spindle with their centers superposed. Figure 1 of 1

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Answer 1

Answer #1

L₁ = L₂

I₁ w₁ = I₂ w₂

1/2 m r² * w₁ = [1/2 m r² + 1/3 m r²] * w₂

1/2 m r² * w₁ = [5/6 m r²] * w₂

1/2 * w₁ = 5/6 * w₂

w₂ = 1/2 * w₁ / (5/6)

= 1/2 * 2.4 / 0.833

angular frequency w₂ = 1.44 rev/s

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Answer 2

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