Questions 18, 19, and 20(no multiple-choice): A playground merry-go-round is ess

Question

Questions 18, 19, and 20(no multiple-choice): A playground merry-go-round is essentially a uniform disk that rotates about a vertical axis through its center. Suppose the merry-go-round has a radius of 2.0 m and a mass of 160 kg; a child weighing 180 N sits at the edge of the merry-go-round. Axis of rotation 2.0 m 180 N Rotational inertia (5 points) 18. What is the final rotational inertia after the child sits at the edge? Show all work. Answer must be correct for credit. (Note: Child can be treated as a point mass and rotational inertias can be added since both have the same rotational axis.)

Explanation / Answer

18. Radius r = 2.0 m

mass of merry go round M = 160 kg

moment of inertia of merry go round I1 = M r2 = 160 x 2x 2 = 640 kg m2

angular velocity of merry go round w1 = 0.75 rev/s = 0.75 x 2 x3.14 rad/s = 4.71 rad/s

weight of the boy w = mg = 180 N

mass of the boy m = 180/9.81 = 18.35 kg

moment of inertia of the boy I2 = m r2 = 18.35 x 2 x 2 = 73.4 kg m2

Final rotational inertia I = I1 + I2  = 640 + 73.4 = 713.4 Kg m2

19. w2 = I1w1 / I

= ( 640 x 4.71)/713.4 = 4.23 rad/s = 0.67 rev/s

  

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