12 . The Earth has more rotational kinetic energy now than did the cloud of gas and dust from which it formed. Where did this energy come from? Figure 10.33 An immense cloud of rotating gas and dust contracted under the influence of gravity to form the Earth and in the process rotational kinetic energy increased. (credit: NASA) This equation is the work-energy theorem for rotational motion only. As you may recall. net work changes the kinetic energy of a system. Through an analogy with translational motion, we dene the term (@th to be rotational kinetic energy KErm for an object with a moment of inertia I and an angular velocity 0): KB\Question 14: Good afternoon everyone, For this discussion, I chose question 14 in chapter III}. '*\"""Suppose a child walks from the outer edge of a rotating merry-go round to the inside. Does the angular velocity of the merry-go-round increase, decrease, or remain the same? Explain your answer.*"* The angular velocity will increase in speed as child moves towards the center of the merry-go-round. Since the child and merry-go-round is an isolated system there is no external torque.. Additionally, there is external force acting on the merry go rounds system's axis, so there is no conservation to solve this question. However, there is an angular momentum that will conserve. As the child moves from edge toward inside of the merry-go-round the moment of inertia will decrease. Since the child is moving inside his distance from center is decreasing. The moment of inertia of child is decreasing as he starts move closer to the center and the nal angular speed of merry-go-round will increase. Finally, the nal angular speed will he more than initial speed as child moves further to the center. _dL T_E Where L = angular momentum since here torque is ZERO 0 _ dL _ at: L = constant L=(Il+l'2)*w 1_l = moment of inertia of merry go round I_2 = moment of inertia of child (11 + 123* \"'1 = (11 +I'23W2 1'2 = mrz Ll] Juan.) of child r = distance of child from center _ (r, \"3):.\" wz _ (gun, !;