A child of mass 53 kg jumps onto the edge of a merry-go-round of mass 160 kg and

Question

A child of mass 53 kg jumps onto the edge of a merry-go-round of mass 160 kg and radius 1.5 m that is initially at rest as sketched in the figure below. While in the air (during her jump), the child's linear velocity in the direction tangent to the edge of the merry-go-round is 13 m/s. What is the angular velocity of the merry-go-round plus child after the child jumps onto the merry-go-round?
rad/s

A child of mass 53 kg jumps onto the edge of a merry-go-round of mass 160 kg and radius 1.5 m that is initially at rest as sketched in the figure below. While in the air (during her jump), the child's linear velocity in the direction tangent to the edge of the merry-go-round is 13 m/s. What is the angular velocity of the merry-go-round plus child after the child jumps onto the merry-go-round?

Explanation / Answer

he angular momentum before and after the child jumps on.

L_i = r*m*v = (1.5m)(53)(13) =1033.5

L_f = [(1/2)M r^2 + m r^2] w = [(0.5)(160kg)(1.5m)^2 + (53kg)(1.5m)^2] w= 299.2 w

Because angular momentum is conserved, set L_i and L_f equal to one another and solve for w.

1033.5= 299.25w

w = 3.45rad/s

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