A uniform circular disk of mass 2 kg and radius 20 cm is rotating clockwise abou

Question

A uniform circular disk of mass 2 kg and radius 20 cm is rotating clockwise about an axis through its center with an angular speed of 30 revolutions per second. A second uniform circular disk of mass 1.5kg and radius 15 cm that is not rotating, is dropped onto the first disk, such that the axis of rotation of the first disk passes through the the center of the second disk. What is the final angular speed of the two disks when they are rotating together?

a. Apply conservation of angular momentum.

b. solve for the final angular speed.

Explanation / Answer

using law of conservation of angular momentum

Li = Lf

0.5*I1*wi^2 = (0.5*(I1+I2)*wf^2)

I1 = 0.5*m1*r1^2 = 0.5*2*0.2^2 = 0.04 kg-m^2

I2 = 0.5*m2*r2^2 = 0.5*1.5*0.15^2 =0.0168 kg-m^2

then

0.5*I1*wi^2 = (0.5*(I1+I2)*wf^2)

0.5*0.04*30^2 = 0.5*(0.04+0.0168)*wf^2

final angular velocity is wf = 25.17 rev/sec

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