A kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ω. Assume that the kid has a mass of 40 kg and is initially running at a speed of 4 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 80 kg and a radius of 2 m. Assume that it rotates without friction. What is the final angular velocity ωf (in radians/s) of the merry-go-round (with the kid riding)?

Problem 4: Amerry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a radius R = 1.1 meters, and a mass M= 286 kg. A small boy of mass m = 41 kg runs tangentially to the merry-go-round at a speed of v = 2.5 m/s, and jumps on. Randomized Variables R = 1.1 meters M= 286 kg m = 41 kg v = 2.5 m/s Part (a) Calculate the moment of inertia of the merry-go-round, in kg · m?. / Correct! I= 178 Part (b) Immediately before the boy jumps on the merry go round, calculate his angular speed (in radians/second) about the central axis of the merry-go-round. / Correct! 227 - ן" Part (c) Immediately after the boy jumps on the merry go round, calculate the angular speed in radians/second of the merry-go-round and boy. / Correct! w2 = 0.5 Part (d) The boy then crawls towards the center of the merry-go-round along a radius. What is the angular speed in radians/second of the merry-…

A uniform disk of mass 7.00m and radius 7.00r can rotate freely about its fixed center like a merry-go-round. A smaller uniform disk of mass m and radius r lies on top of the larger disk, concentric with it. Initially the two disks rotate together with an angular velocity of 14.0 rad/s. Then a slight disturbance causes the smaller disk to slide outward across the larger disk, until the outer edge of the smaller disk catches on the outer edge of the larger disk. Afterward, the two disks again rotate together (without further sliding). (a) What then is their angular velocity about the center of the larger disk? (b) What is the ratio K/K0 of the new kinetic energy of the two-disk system to the system's initial kinetic energy?

Jacob and Sophia are playing with a merry-go-round on a playground. The merry-go-round can be modeled as a flat disk with mass M = 223.0 kg and radius R = 3.3 m that freely rotates horizontally without friction about its center axis. When the merry-go-round is already spinning at 23 rotations per minute, Jacob exerts a constant force F, = 12.3 N tangent to the outer edge of the merry go round in the direction of the merry-go-round's rotation. At the same time Sophia puts her foot at a distance r = 3.1 m from the center, which exerts a constant force of friction Fs = 21.2 N. How long will it take for the merry-go-round to come to a stop?