11.3 Conservation of Angular Momentum

A merry-go-round at a playground is rotating at 4.0 rev/min. Three children jump on and increase the moment of inertia of the merry-go-round/children rotating system by $25 \%$. What is the new rotation rate?

What is the purpose of the small propeller at the back of a helicopter that rotates in the plane perpendicular to the large propeller?

As the rope of a tethered ball winds around a pole, what happens to the angular velocity of the ball?

Explain why stars spin faster when they collapse.

The Sun’s mass is $2.0 \times 10^{30} \text{kg},$ its radius is $7.0 \times 10^{5} \text{km},$ and it has a rotational period of approximately 28 days. If the Sun should collapse into a white dwarf of radius $3.5 \times 10^{3} \text{km},$ what would its period be if no mass were ejected and a sphere of uniform density can model the Sun both before and after?

A diver off the high board imparts an initial rotation with their body fully extended before going into a tuck and executing three back somersaults before hitting the water. If their moment of inertia before the tuck is $16.9 \text{kg} \cdot \text{m}^{2}$ and after the tuck during the somersaults is $4.2 \text{kg} \cdot \text{m}^{2}$, what rotation rate must the diver impart to their body directly off the board and before the tuck if they take 1.4 s to execute th…

A bug of mass 0.020 kg is at rest on the edge of a solid cylindrical disk $\left(M = 0.10 \text{kg}, R = 0.10 \text{m}\right)$ rotating in a horizontal plane around the vertical axis through its center. The disk is rotating at 10.0 rad/s. The bug crawls to the center of the disk. (a) What is the new angular velocity of the disk? (b) What is the change in the kinetic energy of the system? (c) If the bug crawls back to the outer edge of the disk, wh…

A merry-go-round has a radius of 2.0 m and a moment of inertia $300 \text{kg} \cdot \text{m}^{2} .$ A boy of mass 50 kg runs tangent to the rim at a speed of 4.0 m/s and jumps on. If the merry-go-round is initially at rest, what is the angular velocity after the boy jumps on?

Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?

In 2015, in Warsaw, Poland, Olivia Oliver of Nova Scotia broke the world record for being the fastest spinner on ice skates. She achieved a record 342 rev/min, beating the existing Guinness World Record by 34 rotations. If an ice skater extends her arms at that rotation rate, what would be her new rotation rate? Assume she can be approximated by a 45-kg rod that is 1.7 m tall with a radius of 15 c…

A gymnast does cartwheels along the floor and then launches herself into the air and executes several flips in a tuck while she is airborne. If her moment of inertia when executing the cartwheels is $13.5 \text{kg} \cdot \text{m}^{2}$ and her spin rate is 0.5 rev/s, how many revolutions does she do in the air if her moment of inertia in the tuck is $3.4 \text{kg} \cdot \text{m}^{2}$ and she has 2.0 s to do the flips in the air?

A ride at a carnival has four spokes to which pods are attached that can hold two people. The spokes are each 15 m long and are attached to a central axis. Each spoke has mass 200.0 kg, and the pods each have mass 100.0 kg. If the ride spins at 0.2 rev/s with each pod containing two 50.0-kg children, what is the new spin rate if all the children jump off the ride?

A space station consists of a giant rotating hollow cylinder of mass $10^{6} \text{kg}$ including people on the station and a radius of 100.00 m. It is rotating in space at 3.30 rev/min in order to produce artificial gravity. If 100 people of an average mass of 65.00 kg spacewalk to an awaiting spaceship, what is the new rotation rate when all the people are off the station?