Consider a father pushing a child on a playground merry go-round. The system has

Question

Consider a father pushing a child on a playground merry go-round. The system has a moment of inertia of 84.4 kg m2. The father exerts a force on the merry go-round perpendicular to its 1.50 m radius to achieve a torque of 375 N·m. (a) Calculate the rotational kinetic energy (in J) in the merry-go-round plus child when they have an angular velocity of 22.2.rpm. 7 84 (b) using energy considerations, find the number of revolutions the father will have to push to achieve this anguilar velocity starting from rest 0096 revolutions (c) Again, using energy considerations, calculate the force (in N) the father must exert to stop the merry-go-round in nine revolutions 3 16

Explanation / Answer

a) alpha = T / I = 375 / 84.4 = 4.44

rotational KE = 1/2 I w2 = 1/2 * 84.4 * 2.322= 228 J

b) theta = KE / T = 228 / 375 = 0.608 rad

= 0.096 rev

c) F = w / (r * theta)

= 228 / (1.5 * 9 * 2 pi)

force = 2.69 N

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