In the figure the lower disk, of mass 450 g and radius 3.8 c m , is rotating at

Question

In the figure the lower disk, of mass 450g and radius 3.8cm , is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 250g and radius 2.2cm , is initially not rotating. It drops freely down onto the lower disk, and frictional forces bring the two disks to a common rotational speed

In the figure the lower disk, of mass 450g and radius 3.8cm , is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 250g and radius 2.2cm , is initially not rotating. It drops freely down onto the lower disk, and frictional forces bring the two disks to a common rotational speed Find the common speed. RMP? Find the fraction of the initial kinetic energy lost to friction. PERCENT?

Explanation / Answer

conservation of angular momentum-

I1w1 = (I1 + I2)*w2

=> 0.450* .038^2 * 180 = [(0.450* .038^2) + (.250 * .022^2)] * w2

=> w2 = 151.744 rpm

b.

initial Kinetic Energy = 0.5 * I1 * w1^2

= 0.1154 joule

final Kinetic Energy = 0.5 * (I1 + I2) * w2^2

= 0.0973

so, KE lost = 0.0180 joule

so,fraction of the initial kinetic energy lost = 0.0180/ 0.1154 = .1567

15,67%

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