A boy of mass m is standing on the edge of a merry-go-round platform, which is initially rotating with a constant rotational velocity ωi (initial state). The rotational inertia of the merry-go-round is I, and the radius of the platform is r. After the boy steps down from the platform, tangentially to its edge, the merry-go-round continues rotating with a smaller rotational velocity ωf, and the boy continues moving away from the platform with constant speed v (final state).
Derive the expression for ωf in terms of the relevant quantities. Express your answer in terms of I, m, r, v, and ωi.

Select the word from the list that best fits the definition classification of most stars on the h-r diagram

Asteel tube (k=50 w/mk) of inner and outer diameter di = 20mm and do=26mm, respectively, is used to transfer heat from hot gases flowing over the tube (h-hot = 200w/m2k) to cold water flowing through the tube (h-cold = 8000 w/m2k). what is the cold-side overall heat transfer coefficient uc? to enhance heat transfer 16 straight fins of rectangular profile are installed longitudinally along the outer surface of the tube. the fins are equally spaced around the circumference of the tube, each having a thickness of 2mm and a length of 15mm. what is the corresponding overall heat transfer coefficient uc? *solve for uc in both cases*

Is a volume of space that is empty of matter.