A 43-kg boy runs at 4.5 m/s and jumps (tangentially) onto the edge of an initial

Question

A 43-kg boy runs at 4.5 m/s and jumps (tangentially) onto the edge of an initially stationary merry-go-round. The merry-go-round has radius 2.0 m and rotational inertia 2.0×102 kg?m2 , and pivots around its center bearing. Ignore friction.

A. Determine the rotational speed of the merry-go-round after the boy jumps on it. Express your answer to two significant figures and include the appropriate units.

B. Find the change in the boy's kinetic energy. Express your answer to two significant figure and include the appropriate units.

C. Find the change in the kinetic energy of the merry-go-round. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

A)

Using law of conservation of angular momentum

Li = Lf

(m*v*r) = (I1+I2)*w

(43*4.5*2) = ((2*10^2)+(43*2^2))*w

w = 1.04 rad/s is the rotational speed

B) after jumping ,boys KE is 0.5*I*w^2 = 0.5*(43*2^2)*1.04^2 = 93 J

initial KE = 0.5*m*v^2 = 0.5*43*4.5^2 = 435.375 J

Change in KE = 93-435.375 = -342.375 J

C) change in KE of merry go round is dKE = 0.5*I1*w^2 = 0.5*2*10^2*1.04^2 = 108.16 J

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