Rotating disk with spring and mass · PhysicsBowl 2019 #12

Physics · mechanics

Problem

[Figure: TOP VIEW of horizontal disk with a spring and mass attached to a rod passing through its center] A horizontal disk has a spring and a mass attached to a rod passing through its center. The spring has a spring constant of k and the attached mass is m. When the disk is not rotating, the equilibrium length of the spring is d. The disk is now angularly accelerated until it reaches a constant angular velocity of ω. At this angular velocity the length of the spring is now 2d. What is the angular velocity of the disk? (A)

\sqrt{\frac{k}{d}}

(B)

\sqrt{\frac{k}{2m}}

(C)

\sqrt{\frac{2k}{m}}

(D)

\sqrt{\frac{2d}{k}}

(E)

\sqrt{\frac{d}{2k}}

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