Rotating Systems: Energy & Momentum

Under what condition is the angular momentum of a system conserved?

A system consists of two particles rotating about a common axis. Particle A has an angular momentum of $2L$ and particle B has an angular momentum of $-L$. What is the total angular momentum of the system?

A spinning wheel has a constant angular momentum. If a small external torque is applied to the wheel, what will happen to its angular momentum?

A torque of $10 \text{ N} \cdot \text{m}$ is applied to a rotating object for $5 \text{ s}$. What is the angular impulse?

A closed system is rotating with a certain angular momentum. If there are no external torques acting on the system, what happens to the total angular momentum of the system?

A figure skater is spinning with her arms extended. She then pulls her arms in towards her body. What happens to her angular speed?

A complex mechanical system consists of multiple rotating parts with varying moments of inertia and angular speeds. One part increases its moment of inertia while another part decreases its moment of inertia such that the total moment of inertia of the system remains constant. However, an internal motor transfers energ...

A rotating object has an initial moment of inertia $I_1$ and an initial angular speed $\omega_1$. If the moment of inertia is changed to $I_2$ while the angular momentum remains constant, what is the new angular speed $\omega_2$?

A star collapses, decreasing its radius. As a result, its moment of inertia decreases. Assuming no external torques act on the star, how does its angular speed change?

A spinning top experiences a constant torque of $2 \text{ N} \cdot \text{m}$ for $3 \text{ s}$. If its initial angular momentum was $4 \text{ kg} \cdot \text{m}^2/ ext{s}$, what is its final angular momentum?