2. (20 pts) A merry-go-round with moment of inertia of 550 kg m 2 has a boy of m

Question

2. (20 pts) A merry-go-round with moment of inertia of 550 kg m 2 has a boy of mass 45 kg riding in the center of the merry-go-round with an initial angular velocity of 9 revolutions per minute. The boy then travels from the center to the outside rim of the merry-go-round, whose radius is 2 m. (a) (5 pts) Express initial angular velocity in rad/s. (b) (5 pts) Calculate the moments of inertia of the system before and after the boy moves. (c) (5 pts) What is the angular velocity (in rad/s) of the merry-go-round after this motion of the boy? (d) (5 pts)What was the change in the Kinetic Energy?

Explanation / Answer

a) 9 revolutions per minute = 0.942 radians per sec b) initial momentum of intertia = 550 final momentum of inertia = 550 + ( 45*4) = 680 c) 550 * 9 = [ 550 + ( 45*4) ] * w w = 6.78 revolutiosn per minute = 0.71 radians / sec d) change in kinetic energy = 0.5 { [ 680* 0.71*0.71 ] - [550*0.942*0.942] } = - 72.63 J

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