Two circular disks are mounted on frictionless bearings on horizontal axles as s

Question

Two circular disks are mounted on frictionless bearings on horizontal axles as shown in the figure. They are brought together horizontally, stick together and rotate together as one unit. The first disk, with moment of inertia 3.5 kg middot m^2 about its central axis, is set spinning at (+)350 rev/min. The second disk, with moment of inertia 5.2 kg middot m^2 about its central axis, is set spinning at (+)800 rev/min in the same direction as the first. They then come together and rotate as one unit. (a) Let the system include both disks. By assuming that they are displaced in the horizontal direction only and the bearings are frictionless, we are really making which of the following assumptions the angular momentum of the system in the horizontal direction is conserved the kinetic energy of the system is conserved the mechanical energy of the system is conserved there are no unbalanced external torques acting in the horizontal direction on the system (b) What is their angular speed after coupling? rev/min (c) If instead the second disk is set spinning at 800 rev/min in the direction opposite the first disk's rotation (consider the first disk's direction of rotation to be positive and the second disk's direction of rotation to be negative), what is the angular velocity after coupling? rev/min

Explanation / Answer

a)

the angular momentum of the system in the horizontal direction is conserved

b)

I1 W1 + I2 W2 = (I1 + I2)W

speed w after making te subject of the fourmula is

W = I1 W1 + I2 W2 / (I1 + I2)

= ((3.5) * (350) + (5.2) *(800) / (3.5+5.2)

w = 618.96 rev/min

c)

I1 W1 + I2 W2 = (I1 + I2)W

W = I1 W1 + I2 W2 / (I1 + I2)

= ((3.5) * (350) + (5.2) *(-800)) / (3.5+5.2)

= w = -337.35 rev/min

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