A gyroscope has a disk of mass mm and radius of 31 cm that spins at 34 rev/s. The center of mass of the disk is a distance of 15 cm from the point where axis is in contact with the surface of a table. What is the precession angular velocity of the gyroscope in radians per second?

A child jumps to the edge of a carousel, that is in the shape of a circular plate with a radius of 1.3 m and was rotating at an angular velocity of 1.2 s-1 before the chuld jumped on it. The weight of the carousels is 80 kg, the weight of the child is 22 kg. What is their angular velocity after the jump? Later, the child moves closer to the center of the carousel plate by 80 cm. What is the new angular velocity?

An 8.79cm diameter floppy disk rotates at its fastest at 470 rpm.  Part A: Express the angular velocity of the disk in revolutions per seconds?  Part B: What is the time period of this revolution? Use scientific notation for your answer.  Part C: What is the linear velocity of a point at the rim of the disk? Part D: What is the angular velocity at the center of the disk?  Part E: If the disk took 3.2 sec to spin up to 470 rpm from rest, what was the average angular acceleration? How many revolutions did the disk complete within this time? What is the net displacement?  Part F: If you turn off the floppy disk drive and the disk comes to a stop in 6.7 s, what is the average angular acceleration for this period of motion?

A 3.00 kg solid sphere with a radius of 15 cm is rolling without slipping along a horizontal floor. The magnitude of the velocity of the center of mass is 3.00 m/s. What is the ratio of the sphere's rotational kinetic energy to its translational kinetic energy, KErot / KEtrans? 2.

You are riding your bicycle down the road and decide to stop to take in the scenery. Initially, your bicycle tires are rotating at a frequency of 7 times per second. If it takes your bicycle 50 revolutions to come to a full stop, what is the magnitude of the angular acceleration (assume your acceleration is constant). Give your answer in units of radians per second squared

A 10 kg cylindrical barrel with a radius of 0.5 m rotates about a vertical axis of rotation without displacing with an initial angular velocity of 4 rad/s. The rotational inertia of the cylindrical barrel is 0.3mr2 and rain begins to fill the barrel with water as it rotates. If the barrel accumulates 4 kg of water, calculate the new angular velocity of the barrel.

Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.70 m . The merry‑go‑round is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the 28.0 kg child moves to the center of the merry‑go‑round, what is the new angular velocity in revolutions per minute? Ignore friction, and assume that the merry‑go‑round can be treated as a solid disk and the children as point masses.   final angular velocity:   rpm

A playground merry-go-round has a mass of  133kg and a radius of  1.82m and it is rotating with an angular velocity of  0.424rev/s. What is its angular velocity after a 29-kg child gets onto it by grabbing its outer edge? The child is initially at rest.

A playground uniform merry-go-round has a mass of 110 kg and a radius of 1.90 m and it is rotating at a rate of 40 revolutions per minute. a) What is its angular velocity [ in rad/s] after a 20-kg child gets onto it by grabbing its outer edge? The child is initially standing on the ground. b) What is the new angular velocity [in rad/s] after the child moves to the center of the merry-go-round?

A figure skater does a single-axle jump, turning 1.5 revolutions while in the air. The skater is in the air for 0.48 s, and his hands are located 0.69 m from the rotation axis. a) What is the angular velocity (in rad/s) of the skater during the leap? b) What is the linear tangential speed (in m/s) of the skater's hand? c) What is the centripetal acceleration (in m/s^2) of each of the skater's hands during the jump?