The Wobbling Hula Hoop · AI Generator #GEN-BA433C1D

Physics · mechanics

Problem

A hula hoop of radius R=0.50  mR = 0.50\;\text{m} and mass M=1.2  kgM = 1.2\;\text{kg} is rolling without slipping down a rough inclined plane with angle θ=30°\theta = 30°. When the hoop reaches the bottom with speed v0=4.0  m/sv_0 = 4.0\;\text{m/s}, it encounters a small obstacle that causes it to start wobbling. The wobbling motion can be modeled as the hoop's center of mass executing small oscillations perpendicular to its direction of motion while the hoop continues to roll forward. During the wobbling motion, the hoop's center of mass oscillates with amplitude A=0.080  mA = 0.080\;\text{m} and period T=0.60  sT = 0.60\;\text{s}. At the instant when the center of mass is at maximum displacement from the centerline, what is the magnitude of the angular momentum of the hoop about a point on the ground directly below the hoop's center of mass at that instant? Treat the hula hoop as a thin ring with moment of inertia I=MR2I = MR^2 about its center.

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