The Wobbling Bicycle Wheel · AI Generator #GEN-78178581

Physics · mechanics

Problem

A bicycle wheel of radius R=0.35  mR = 0.35\;\text{m} and mass m=2.0  kgm = 2.0\;\text{kg} is spinning horizontally on a frictionless vertical axle at angular velocity ω0=15  rad/s\omega_0 = 15\;\text{rad/s}. The wheel can be modeled as a thin ring. A small piece of clay of mass M=0.40  kgM = 0.40\;\text{kg} is dropped vertically onto the rim of the wheel and sticks to it. The clay hits the wheel with a vertical velocity of v=3.0  m/sv = 3.0\;\text{m/s} downward just as it contacts the rim. Immediately after the collision, find the angular velocity of the wheel-clay system about the original vertical axis.

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