The 170 lb ice skater with arms extended horizontally spins about a vertical axi

Question

The 170 lb ice skater with arms extended horizontally spins about a vertical axis with a rotational speed of 1 rev/sec. Estimate his rotational speed if he fully retracts his arms, bringing his hands very close to the centerline of his body. As a reasonable approximation, model the extended arms as uniform slender rods, each of which is 27 in. long and weighs 16 lb. Model the torso as a solid 138-lb cylinder 13 in. in diameter. Treat the man with arms retracted as a solid 170 lb cylinder of 13 in. diameter. Neglect friction at the skate-ice interface. (Hint: You'll need to use the parallel-axis theorem to figure out the moment of inertia of the extended arms.)
___________________________ rev/s

The 170 lb ice skater with arms extended horizontally spins about a vertical axis with a rotational speed of 1 rev/sec. Estimate his rotational speed if he fully retracts his arms, bringing his hands very close to the centerline of his body. As a reasonable approximation, model the extended arms as uniform slender rods, each of which is 27 in. long and weighs 16 lb. Model the torso as a solid 138-lb cylinder 13 in. in diameter. Treat the man with arms retracted as a solid 170 lb cylinder of 13 in. diameter. Neglect friction at the skate-ice interface. (Hint: You'll need to use the parallel-axis theorem to figure out the moment of inertia of the extended arms.) ___________________________ rev/s

Explanation / Answer

I1 = (1/2)*170*6.5*6.5 = 3591.25

initial angular momentum Li = I1*w1 = 3591.25*1 = 3591.25

I2 = ((1/2)*138*6.5*6.5) + (2*(1/3)*16*27*27) = 10691.25

final angular momentum Lf = I2*w2 = 10691.25*w2

Lf = Li

10691.25*w2 = 3591.25

w2 = 0.336 rad/s

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