Q Two circular disks are mounted on frictionless bearings on horizontal axles as
ID: 1417344 • Letter: Q
Question
Q
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-m^2 about its central axis, is set spinning at (+)350 rev/min. The second disk, with moment of inertia 5.2 kg-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/minExplanation / Answer
uses the conservation of angular momentum, so the change in angular momentum will be zero
we take the counterclockwise direction to be positive
w (omega) is angular velocity
i is the moment of inertia
A ) the angular momentum of the system in the horizontal direction is conserved
for b)
angular momentum of the first disk + angular momentum of the second disk = angular momentum of the combined disk
to get the combined moment of inertia we simply add the two individual moments because the moment of inertia is to angular physics as mass is to transitional physics
iw_1 + iw_2 = iw_final
(3.5)(350)+(5.2)(800)=(3.5+5.2)w
w = 618.96 rev/min
for c)
it is the same, but the second disk is rotating in the clockwise, or negative, direction
(3.5)(350)+(5.2)(-800)=(3.5+5.2)w
w = -337.35 rev/min
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