Item 8 Imagine two disks on a shared (frictionless) axle. In the initial state t

Question

Item 8 Imagine two disks on a shared (frictionless) axle. In the initial state the lower disk, of mass 430 g and radius 3.8 cm Part A is rotating at 180 rpm, while the upper disk, of mass 270 g and radius 2.5 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 inal rotational speed. Assume that no external torques áct 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). (Figure 1) Find the final common frequency in rpm Express your answer using two significant figures ?? rpm Figure 1 of 1 Submit Provide Feedback

Explanation / Answer

for lower disk,

I1 = M R^2 / 2 = (0.430)(0.038^2)/2

I1 = 3.1046 x 10^-4 kg m^2

Upper disk,

I2 = (0.270)(0.025^2)/2 = 8.4375 x 10^-5 kg m^2

Applying angular momentum conservatin,

I1 w1 + I2 w2 = (I1 + I2) w

(3.1046 x 10^-4)(180) + (8.4375 x 10^-5 x 0 )

= (3.1946 x 10^-4 + 8.4375 x10^-5) w

w = (3.1046 x 180) / (3,94835)

w = 141.5 rpm

Ans: 140 rpm

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