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 2 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 120 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)

The figure shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance of d = 0.922 m, and rotating with an angular speed of 90.8 rad/s. The bullet first passes through the left disk and then through the right disk. It is found that the angular displacement between the two bullet holes is = 0.360 rad. From these data, determine the speed of the bullet. Number i Bullet Units 19 kd + Motor

A bullet of mass m=2.0g is moving horizontally with a speed of 500.0m/s. The bullet strikes and  becomes embedded in the edge of a solid disk of mass M=3.2kg and radius R=0.5m. The cylinder is  free to rotate around its axis and is initially at rest. What is the angular velocity of the disk  immediately after the bullet is embedded?

Earth has a mass of 5.97×1024 kg and a radius of 6.37×106 m. The period of Earth’s rotation is 24 hours (i.e., it rotates on its axis once every 24 hours). Imagine that Earth is compressed down to half of its current radius, while its angular momentum is conserved and it retains all of its mass. Treat the Earth as a solid sphere, whose moment of inertia is I = 25 M R 2 .   (a) What is the final rotation period, in hours? (b) What is the change in Earth’s rotational kinetic energy during this process? Give your answer in units of Joules.