A uniform circular disk of mass 2.00 kg and radius 20.0 cm is rotating clockwise

Question

A uniform circular disk of mass 2.00 kg and radius 20.0 cm is rotating clockwise about an axis through its center with an angular speed of 30.0 revolutions per second. A second uniform circular disk of mass 1.50 kg and radius 15.0 cm that is not rotating is dropped onto the first disk so that the axis of rotation of the first disk passes through the center of the second disk. What is the final angular speed of the two disks when they are rotating together? a. What quantity is conserved? b. Apply the appropriate conservation law. c. Solve for the final angular speed.

Explanation / Answer

(a)

angular momentum is conserved

(b)

when no external torque acts on the system , the net angular momentum remains constant

(c)

initial angular momentum Li = I1*w1 + I2*w2

I1 = moment of inertia of first disk = (1/2)*m1*r1^2

w1 = initial speed of disk 1 = 30 rps

w2 = initial speed of disk 2 = 0

I2 = moment of inertial of second disk

final angular momentum Lf = (I1+I2)*wf

Lf = Li

((1/2)*m1*r1^2 + (1/2)*m2*r2^2)*wf = (1/2)*m1*r1^2*w1

(2*0.2^2 + 1.5*0.15^2)*wf = 2*0.2^2*20

wf = 14.1 revolutions per second

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