Imagine two disks on a shared (frictionless) axle. In the initial state the lowe

Question

Imagine two disks on a shared (frictionless) axle. In the initial state the lower disk, of mass 460 g and radius 3.9 cm, is rotating at 180 rpm, while the upper disk, of mass 280 g and radius 2.1 cm, is held at rest. Now, the upper disk is pushed down onto the lower disk, and the rub against each other until they come to a common final rotational speed. Assume that no external torques act on the system (the only torques involved are due to the friction between the disks while the upper disk is speeding up and the lower disk is slowing down, before they become stuck together and rotate as one unit). Find the final common frequency in rpm. Express your answer using two significant figures.

Explanation / Answer

Apply conservation of angular momentum

Li = Lf

If*Wf = Ii*wi

wf = Ii*wi/If

Here If = (I1 + I2) = 0.5*m1*r1^2 + 0.5*m2*r2^2 = 0.5*0.46*0.039^2 +0.5*0.28*0.021^2 = 0.00041157

Ii = I1 = 00034983

wf = 00034983*180 rpm/0.00041157 = 152.99 rpm

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