Question

Two children (m = 34.0 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 0.42 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

Answer 1

w = 0.42 * 2 pi = 2.64 rad/s

a) L = 1/2 M r² w + 2 m r² w

= (1/2 * 174 * 1.4² * 2.64) + (2 * 34 * 1.4² * 2.64)

= 802 kg.m²/s

b) Total KE = 1/2 w² (1/2 M r² + 2 m r²)

= 1/2 * 2.64² * ( 1/2 * 174 * 1.4² + 2 * 34 * 1.4² )

= 1058 J

c) From conservation of angular momentum

L = w' ( 1/2 M r² + 2 m (r/2)² )

802 = w' ( 1/2 * 174 * 1.4² + 2 * 34 * (1.4/2)² )

w' = 3.93 rad/s