# 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:

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

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

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

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

79% (243 ratings) ###### Problem Details

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)?

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