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Question: "At the beginning of each term, a physics professor named Dr. Zeus shows the class his expectations of them through a demonstration that he calls "Lesson #1." He stands at the center of a turntable that can rotate without friction. He then takes a 2-kg globe of the earth and swings it around his head at the end of a 0.8-m chain. The world revolves around him every 3 s, and the professor and the platform have a moment of inertia of 0.5 kg m^2 . (a) What is the angular speed of the professor? (b) What is the total kinetic energy of the globe, professor, and platform?"

Since there is no external torque acting on the system, I figured that the momentum must be conserved. If the professor starts at rest therefore, then the spinning of the globe must cause the platform to spin to counteract it. So I calculated the angular momentum of the globe, treating it like a point mass, using L = m*r^2*w , I found the momentum of the globe to be 2.68 kg*m^2/s. Using conservation of angular momentum, I then use L(globe) = L(platform+professor), L(globe) = Iw, and found w to be 5.36 /s.

For part (b), I figured basically just treat the professor and platform as one system, and use the kinetic energy formulas ( k = 1/2 I*w^2 for the platform, k = 1/2 m*r^2*w for the globe), and summed them to get 8.52 J.

I think I have done this well, but, am I completely off? Some input would be greatly appreciated.