Two children, ( m = 33.0 kg each) stand opposite each other on the edge of a mer

Question

Two children, (m = 33.0 kg each) stand opposite each other on the edge of a merry-go-round. The merry-go-round, which has a mass of 1.74 102 kg and a radius of 1.4 m, is spinning at a constant rate of 0.38 rev/s. Treat the two children and the merry-go-round as a system.

(a) Calculate the angular momentum of the system, treating each child as a particle. (Give the magnitude.)   kg · m2/s

(b) Calculate the total kinetic energy of the system. J.

(c) Both children walk half the distance toward the center of the merry-go-round. Calculate the final angular speed of the system. rad/s
rad/s

Explanation / Answer

a) moment of inertia of system, i = 0.5*174*1.4^2 + 2*33*1.4^2 = 299.9 kg m2

Angular momentum = iw = 299.9*0.38*2pi = 716 kgm2/s

b)Total KE = 0.5i w^2 = 0.5*299.9*(0.38*2 pi)^2 = 854.8 J

C) new moment of inertia = 0.5*174*1.4^2 + 2*33*0.7^2 =202.86 kgm2

new angular speed w ' = Anular momentum / new moment of inertia

=716/202.86

= 3.53 rad/s

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