Imagine two disks on a shared (frictionless) angle. In the initial state the low

Question

Imagine two disks on a shared (frictionless) angle. In the initial state the lower disk, of mass 410 g and radius 4.0 cm, is rotating at 180 r_xn. while the upper disk, of mass 270 g and radius 2.1 cm. is held at rest. Now, the upper disk is pushed down onto the lower disk, and they rub against each other until they come to a common final retaional 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 becomes stuck together and rotate as one unit) Find the final common frequency in rpm. Express your answer using two significant figures.

Explanation / Answer

Initial Moment of inertia

Iinitial=(1/2)MupperRupper2 =(1/2)(0.41)(0.04)2=3.28*10-4 Kg-m2

Final Moment of inertia

Ifinal=(1/2)MupperRupper2+(1/2)MlowerRlower2=(1/2)(0.41)(0.04)2+(1/2)*0.27*0.0212

Ifinal = 3.875*10-4 Kg-m2

By Conservation of angular momentum

Li=Lf

IintialWinitial = IfinalWfinal

(3.28*10-4 )(180)=(3.875*10-4)Wfinal

Wfinal=152.3 rpm

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