First slide

Rotational motion

Question

A disk with moment of inertia I₁ rotates about a frictionless, vertical a:de with angular speed $ω_{1}$ . A second disk, this one having moment of inertia l₂ and initially not rotating, drops onto the first disk (figure). Because of friction between the surfaces, the two eventually reach the same angular speed $ω_{f}$ The value of $ω_{f}$ is

Moderate

A

$\frac{I_{1} + I_{2}}{I_{1}} ω_{i}$
B

$\frac{I_{1}}{I_{1} + I_{2}} ω_{i}$
C

$\frac{I_{1} + I_{2}}{I_{2}} ω_{i}$
D

$\frac{I_{1}}{I_{2}} ω_{i}$

Solution

From conservation of angular momentum for the isolated system of two disks:
$(I_{1} + I_{2}) ω_{f} = I_{1} ω_{i} or ω_{f} = \frac{I_{1}}{I_{1} + I_{2}} ω_{i}$

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