Use the before-and-after figure. A student on a freely turning stool pulls two masses inward, and no external torque acts about the axis. What happens to the angular velocity?

The figure shows a diver rotating about a frictionless axis while tucking. No external torque acts about the axis. What change in angular velocity follows?

In the figure, a gymnast opens her arms while rotating on a low-friction pivot. No external torque acts about the axis. What happens to her angular velocity?

The figure shows a student on a frictionless rotating stool moving held masses outward. No external torque acts about the axis. What happens to angular velocity?

A rider on a frictionless merry-go-round moves inward as shown. No external torque acts about the center. What happens to the angular velocity?

The figure shows a rotating gas cloud contracting with no external torque about its axis. What happens to its angular velocity?

A robot on a frictionless turntable folds its arms as shown, and no external torque acts about the axis. How does its angular velocity change?

A puck moves in a circle on a frictionless table while its string is pulled through a hole at the center. The figure shows the change. What happens to angular velocity?

A skater has $I=4.0\text{kg}\cdot {\text{m}}^2$ and omega=1.5 rad/s with arms out. She pulls in to $I=1.2\text{kg}\cdot {\text{m}}^2$. No external torque acts about her spin axis. What is ${\omega }_f$?

A diver's rotational inertia changes from $2.5\text{kg}\cdot {\text{m}}^2$ to $0.90\text{kg}\cdot {\text{m}}^2$ while his angular velocity is initially 1.8 rad/s. No external torque acts. What is ${\omega }_f$?

A student on a frictionless stool has $I=6.0\text{kg}\cdot {\text{m}}^2$ and omega=0.75 rad/s. She pulls masses inward so $I=1.5\text{kg}\cdot {\text{m}}^2$. What is her final angular velocity?

A child already on a frictionless merry-go-round walks toward the center. The system's I changes from $120\text{kg}\cdot {\text{m}}^2$ to $96\text{kg}\cdot {\text{m}}^2$ while ${\omega }_i=0.80\text{rad/s}$. What is ${\omega }_f$?

A turntable with $I=0.20\text{kg}\cdot {\text{m}}^2$ spins at 12 rad/s. A nonspinning disk with $I=0.10\text{kg}\cdot {\text{m}}^2$ drops onto it and sticks. The axle is frictionless. What is the final angular velocity?

A rotating system has $I_i=5.0\text{kg}\cdot {\text{m}}^2$ and ${\omega }_i=2.4\text{rad/s}$. After an internal change, ${\omega }_f=6.0\text{rad/s}$ and no external torque acts. What is $I_f$?

A skater extends her arms so her spin slows from 5.0 rad/s to 2.0 rad/s. Her initial rotational inertia is $1.8\text{kg}\cdot {\text{m}}^2$, and external torque is negligible. What is $I_f$?

A skater pulls her arms inward on nearly frictionless ice. Her angular momentum stays constant, but her rotational kinetic energy increases. What supplies the extra energy?

A spinning disk and a second disk at rest stick together on a frictionless axle. Total angular momentum is conserved, but rotational kinetic energy decreases. Where does the missing energy go?

A child on a frictionless merry-go-round walks outward from the center, and the ride slows. With no external torque, what happens to rotational kinetic energy?

Which statement best connects angular momentum and rotational kinetic energy for a system whose shape changes with no external torque?

A stool-and-student system changes from $I=6.0\text{kg}\cdot {\text{m}}^2$ to $I=2.0\text{kg}\cdot {\text{m}}^2$ with no external torque. What happens to rotational kinetic energy, and why?

Four systems are observed for a few seconds. In which system is angular momentum about the spin axis conserved?

A skater on rough ice keeps her arms fixed while friction from the ice slows her spin. Is her angular momentum about the spin axis conserved?

A lump of clay lands on a spinning turntable and sticks. The axle is frictionless. For which system is angular momentum about the axle conserved during the collision?

A person spinning on a stool reaches out and pushes on a wall, changing her spin. Is angular momentum of the person-stool system conserved during the push?

A satellite coasts around a planet with thrusters off and drag ignored. About the planet's center, is the satellite's angular momentum conserved?