Question

Three children are riding on the edge of a merry-go-round that has a disk of mass 102 g, radius 1.9 m, and is spinning at 16 rpm. The children have masses of 23.2 kg, 26.4 kg, and 33.4 kg. If the child who has a mass of 26.4 kg moves to the center of the merry-go-round, what is the new magnitude of angular velocity in rpm?

(3%) Problem 18: Three children are riding on the edge of a merry-go-round that is a disk of mass 102 kg, radius 1.9 m, and is spinning at 16 rpm. The children have masses of 23.2 kg, 26.4 kg, and 33.4 kg. Randomized Variables M = 102 kg m; = 23.2 kg m2 = 26.4 kg mz = 33.4 kg r=1.9 m f= 16 rpm * If the child who has a mass of 26.4 kg moves to the center of the merry-go-round, what is the new magnitude of angular velocity in rpm? Grade Summary Deductions 10% Potential 90% HOME o E sino cotan atan cosh cos t an() a sino acos acotan sinh tanh( cotanh0 Degrees Radians ( 7 8 4 5 * 1 2 + - 0 VO BACKSPACE 9 6 3 . Submissions Attempts remaining: 2 (10% per attempt) detailed view 10% END CLEAR Submit Hint Feedback I give up! Hints: 5% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback.

Answer 1

By conservation of angular momentum,

final angular momentum = initial angular momentum

i1w1 = i2w2 whew w1,w2 are the initial and final angular speeds, and i1,i2 are initial and final meet of inertia.

(0.5*102*1.9^2 + 23.2*1.9^2 + 33.4*1.9^2)*w2 = (0.5*102*1.9^2 + 23.2*1.9^2 + 33.4*1.9^2 +26.4*1.9^2)*16

w2 = 19.93 rpm answer