1. Use conservation of linear momentum during the collision: $m_1v_1 = (m_1 + m_2)v_f$. 2. Use conservation of energy for the swing: $\frac{1}{2}(m_1 + m_2)v_f^2 = (m_1 + m_2)gh$.

1. Identify the system as the colliding disks. 2. Recognize that the torques are internal. 3. Apply $L_{initial} = L_{final}$ using $L=I\omega$ for each disk.

1. Recognize that angular momentum is conserved. 2. Apply $L_{initial} = L_{final}$. 3. Express L as $I\omega$ and solve for the unknown angular velocity or moment of inertia.

The angular momentum of the system changes, as described by $\tau = \frac{dL}{dt}$.

Its speed increases to conserve angular momentum.

Their moment of inertia decreases, and their angular speed increases to conserve angular momentum.

The block and bullet system gains momentum, and the system begins to swing upwards.

The angular velocity must increase to conserve angular momentum, assuming no external torque.

Linear Momentum: $p=mv$, translational motion | Angular Momentum: $L=I\omega$, rotational motion

Elastic: Kinetic energy is conserved, Angular momentum is conserved | Inelastic: Kinetic energy is not conserved, Angular momentum is conserved