Could you please help with this problem, thank you. The 165-lb ice skater with a

Question

Could you please help with this problem, thank you.

The 165-lb ice skater with arms extended horizon tally spins about a vertical axis with a rotational speed of 1 rev/sec. Estimate his rotational speed N if he fully retracts his arms, bringing his hands very close to the centerline of his body. As a rea- sonable approximation, model the extended arms as uniform slender rods, each of which is 27 in. long and weighs 15 lb. Model the torso as a solid 135-lb cylinder 13 in. in diameter. Treat the man with arms retracted as a solid 165-lb cylinder of 13-in. diameter. Neglect friction at the skate-ice interface.

Explanation / Answer

Initial moment of inertia = (1/2 * 135 * 6.5 * 6.5) + 2 * (1/3 * 15 * 37 * 37)

                                      =   16541.875 lb.in2

Final moment of inertia =   (1/2 * 165 * 6.5 * 6.5)

                                       = 3485.625 lb.in2

Applying conservation of angular momentum

=>   16541.875   * 1   =   3485.625 * w

=> w   = 4.75 rev/sec                   ----------------------> final rotational speed

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