Problem: Disk A, with a mass of 2.0 kg and a radius of 40 cm, rotates clockwise about a frictionless vertical axle at 20 rev/s. Disk B, also 2.0 kg but with a radius of 30 cm, rotates counterclockwise about the same axle, but a greater height than disk A, at 20 rev/s. Disk B slides down the axle until it lands on top of disk A, after which they rotate together.After the collision, what is magnitude of their common angular velocity (in rev/s)?

FREE Expert Solution

In this problem, we're going to use the law of conservation of angular momentum, which is given by:

$\boxed{{\mathbf{I}}_{\mathbf{A}}{\mathbf{\omega }}_{\mathbf{A}}\mathbf{+}{\mathbf{I}}_{\mathbf{B}}{\mathbf{\omega }}_{\mathbf{B}}\mathbf{=}\mathbf{(}{\mathbf{I}}_{\mathbf{A}}\mathbf{+}{\mathbf{I}}_{\mathbf{B}}\mathbf{)}\mathbf{\omega }}$, where I is the moment of inertia and ω is the angular velocity. 

The moment of inertia of a disk about the axis is:

$\boxed{\mathbf{I}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{M}{\mathbf{R}}^{\mathbf{2}}}$

Since disk B is rotating counterclockwise, we'll take its angular omentum to be negative.

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