Question

A uniform disk turns at 3.6 rev/s around a frictionless spindle. A non rotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk . They then both turn around the spindle with their centers superposed.

What is the angular frequency in rev/s of the combination?
please express answer in proper significant figures and rounding.

Answer 1

ω₁ = 2.2 rev/s

Step-by-step explanation:

Conservation of angular momentum

moment of inertia uniform disk is ½mR²

moment of inertia uniform rod about an end mL²/3

We can think of our rod as two rods of mass m/2 and length R

L = ½mR²ω₀

L = (½mR² + 2(m/2)R²/3)ω₁

ω₁ = ω₀(½mR² / (½mR² + mR²/3))

ω₁ = ω₀(½ / (½ + 1/3))

ω₁ = 0.6ω₀

ω₁ = 2.16