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Angular Analogue of Linear Momentum

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Question

A horizontal disk of moment of inertia 4.25 kg- $m^{2}$ with respect to its axis of symmetry is spinning counter clockwise at 15 revolutions per second about its axis, as viewed from above. A second disk of moment of inertia 1.80kg- $m^{2}$ with respect to its axis of symmetry is spinning clockwise at 25 revolutions per second as viewed from above about the same axis and is dropped on top of the first disk. The two disks stick together and rotate as one about their axis of symmetry. The new angular velocity of the system as viewed from above is close to.

A

18 revolutions/second and clockwise

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B

18 revolutions/second and counter clockwise

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C

3 revolutions/second and clockwise

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D

3 revolutions/second and counter clockwise

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Solution

The correct option is C 3 revolutions/second and clockwise
Take anticlockwise positive
$I_{1} ω_{1} + I_{2} ω_{2} = I ω 4.25 \times 15 - 1.80 \times 25 = 6.05 \times ω ω = 3$ revolutions/second and clockwise

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