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March 27, 2017

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A lazy Susan consists of a heavy plastic disk mounted on a frictionless bearing resting on a vertical shaft through its center. The cylinder has a radius R = 10 cm and mass M = 0.24 kg. A cockroach (mass m = 0.015 kg) is on the lazy Susan, at a distance of 10 cm from the center. Both the cockroach and the lazy Susan are initially at rest. The cock&roach then walks along a circular path concentric with the axis of the lazy Susan at a constant distance of 10 cm from the axis of the shaft. If the speed of the cockroach with respect to the lazy Susan is 0.01 m/s, what is the speed of the cockroach with respect to the room?

  • physics - ,

    Assume the total angular momentum remains zero (due to frictionless bearing). If the angular velocity of the lazy susan is w, its angular momentum is I*w, where I = (1/2)M*R^2

    The angular momentum of the kokroach is equal and opposite to that of the lazy susan.

    I*w = m*R*v
    where v is the speed of the kokroach with respect to the room, m is the roach mass, and R = 0.10 m.
    You also need to use the equation
    v - R*w = 0.01 m/s
    for the relative velocity

    Solve for v.

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