The yo-yo in Figure 19 is made up of two disks of radius r = 3 cm and an axle of radius

Chapter 15, Problem 47

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The yo-yo in Figure 19 is made up of two disks of radius r = 3 cm and an axle of radius b = 1 cm. Each disk has mass M1 = 20 g, and the axle has mass M2 = 5 g.(a) Use the result of Exercise 45 to calculate the moment of inertia I of the yo-yo with respect to the axis of symmetry. Note that I is the sum of the moments of the three components of the yo-yo. (b) The yo-yo is released and falls to the end of a 100-cm string, where it spins with angular velocity . The total mass of the yo-yo is m = 45 g, so the potential energy lost is PE = mgh = (45)(980)100 g-cm2/s2. Find using the fact that the potential energy is the sum of the rotational kinetic energy and the translational kinetic energy and that the velocity v = b since the string unravels at this rate.