A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg • m2 is rotating freely with an angular speed of 1.0 rad/s. Two people, each of mass 60 kg, are standing right outside the edge of the merry-go-round and suddenly step onto the edge with negligible speed relative to the ground. What is the angular speed of the merry-go-round right after the two people have stepped on?

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 740 n/m. it is initially at rest on an inclined plane that is at an angle of theta= 26 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is uk = 0.17. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. the block's initial mechanical energy is 9.472 j.b. if the spring pushes the block up the incline, what distance l in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.