In the diagram disk 1 has a moment of inertia of 4.2 kg In the diagram disk 1 ha

Question

In the diagram disk 1 has a moment of inertia of 4.2 kg

In the diagram disk 1 has a moment of inertia of 4.2 kg A m^2 and is rotating in the counterclockwise direction with an angular velocity of 6.5 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular velocity of 9.3 rad/s falls from above onto disk 1. The two then rotate as one in the clockwise direction with an angular velocity of 2.0 rad/s. Determine the moment of inertia of disk 2. ________kg A m^2

Explanation / Answer

I1 = moment of inertia of first disk = 4.2 kg m2

I2 = moment of inertia of second disk = ?

(taking clockwise direction as positive and counterclockwise as negative )

W1 = angular speed of first disk = - 6.5 rad/s      

W2 = angular speed of second disk = 9.3 rad/s

Wf   = final angular speed when disks move together in same clockwise direction = 2 rad/s

Using Conservation of angular momentum ::

I1 W1 + I2 W2 = (I1 + I2 ) Wf

(4.2)(-6.5) + I2 (9.3) = (4.2 + I2 ) 2

-27.3 + 9.3 I2 = 8.4 + 2 I2

9.3 I2 - 2 I2 = 8.4 + 27.3

7.3 I2 = 35.7

I2 = 4.89

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