A 200-kg, 2.0-m-radius, merry-go-round in the shape of a flat, uniform, circular disk parallel to level ground is rotating at 1.2 cycles/second about an axis through its center of mass and perpendicular to the ground. A 50-kg boy jumps onto the edge of the merry-go round and lands at a fixed point. What is the angular velocity of the merry-go-round after the boy lands on it? Hint:  = (1/2)mR2

A 0.02 kg mass red object (bead) is moving at a speed of 10.0 m/s when it sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about its axis through its center and has a mass of 0.5 kg , a radius of 0.25 m and is initially at rest. I = 1/2MR​2^2 a) What is the angular velocity of the system after the collision? b) How much kinetic energy is lost in the collision? c) If the angular position of the Cylinder varies as θ(t)=3.2t-t​^2 ​find the centripetal acceleration of the red object (bead). d) A cord is now wrapped around the cylinder. Use the work energy theorem to find the angular velocity of the cylinder after 5.0m of cord have been removed by a 40N Force. e) If the 40N force on the cord is replaced by a 40-N weight, what is the angular velocity of the cylinder after 5.0m of cord has unwound?

A sanding disk with a rotational inertia of 1.2 x 10-3kgm2 is attached to an electric drill whose motor delivers a torque of 16 Nm.  If the torque is applied for 25 ms and the disk starts from rest, what is the magnitude of the angular velocity of the sanding disk?  Use the rotational version of the Impulse Momentum Theorem.  Take note of the time units.

A 5.0-m radius playgorund merry-go-round with a moment of inertia of 2000 Kg*m2is rotating freely with an angular speed of 2.0 rad/s. Two people, each having a mass of 60 Kg, are standing right outside the edge of the merry-go-round and step on it with negligible speed. what is the angular speed of the mery go round right after the two people have stepped on?