a 40 kg child stands at the edge of a uniform cylinder ... Question A 40 Kg chil

Question

a 40 kg child stands at the edge of a uniform cylinder ... Question A 40 Kg child stands at the edge of a uniform cylinder Merry-Go-Round of mass 80 kg and radius 2m initially rotating at 4 rad/s. If the child walks radially on the Merry-Go-Round to its center determine the angular velocity of the system. Comment A 40 Kg child stands at the edge of a uniform cylinder Merry-Go-Round of mass 80 kg and radius 2m initially rotating at 4 rad/s. If the child walks radially on the Merry-Go-Round to its center determine the angular velocity of the system.

Explanation / Answer

The angular moment of the system remains constant at all points of time, as given by the law of conservation of angular momentum.

But the angular velocity along with the moment of inertia changes.

initial moment of inertia I1 = Mr2 /2 + mr2 = 80x 22/2 + 40x 22 = 320 kgm2

1 = 4 rad/s

Final moment of inertia I2 = Mr2/2 + m(0)2 = 80 x 22/2 + 0 = 160 kgm2

Anglluar momentum I = constant

So, I11 = I22

320 x 4 = 160 x 2

2 = 8 rad/sec

so the angular velocity increases as the child goes to the centre.

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