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A spoked wheel with a radius of 44.0 cm and a mass of 1.90 kg is mounted horizontally on frictionless bearings. JiaJun puts his 0.550-kg guinea pig on the outer edge of the wheel. The guinea pig begins to run along the edge of the wheel with a speed of 18.0 cm/s with respect to the ground. What is the angular velocity of the wheel? Assume the spokes of the wheel have negligible mass.

Honestly, I don't know how to calculate this, I have been trying to figure out but I have been guessing, and am sure they aren't write because they gave me wrong answers. Need help thank you in advance.

  • physics -

    Since the bearings are frictionless, the total angular momentum of wheel and guinea pig remains zero, as they rotate in opposite directions.

    0.18 m/s*0.550kg*0.44m
    = 0.04356 kg m^2/s
    = -Iwheel*w

    The moment of inertia of the wheel is
    Iwheel = M*R^2 = 1.90*(0.44)^2
    = 0.3678 kg*m^2. Therefore
    w = -0.118 rad/s

    The minus sign indicates that it is turning in the opposite direction from the guinea pig.

  • physics -

    Thank you so much; I really appreciate it!

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