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physics

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an ice skater spins about a vertical axis at an angular speed of 15 rad/s when her arms are outstreched . she then quickly pulls her arms into her sides in a very small time interval so that the frictional force due to ice are negligible.her initial moment of inertia about the axis of rotation is 1.72kgm^2 and her final moment of inertia is 0.061kgm^2. what is the change in her angular speed? what is the change in her kinetic energy?explain this change in kinetic energy.

  • physics - ,

    Because angular momentum is conserved,
    I*w = (Moment of intertia)*(angular speed) remains constant
    Therefore
    1.72*(15 rad/s)= 0.061*(final angular speed)
    Final angular speed = 15*1.72/0.061
    = 423 rad/s

    Kinetic energy = (1/2)*I*w^2
    increases by the same (w2/w1) factor, sinc I*w is constant.

    The added kinetic energy comes from work done by the skater pulling in her arms and free leg.

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