Linear momentum: mass in linear motion, conserved when no external forces act. Angular momentum: rotational inertia in rotational motion, conserved when no external torques act.

Linear velocity: changes as a planet orbits (faster closer to the star). Angular velocity: constant, ensuring equal areas are swept out in equal times (Kepler's 2nd Law).

1: Identify initial and final states. 2: Determine if external torque is zero. 3: Apply $L_{initial} = L_{final}$. 4: Solve for the unknown.

1: Skater starts spinning with arms out (high $I$, low $\omega$). 2: Skater pulls arms in (low $I$). 3: Angular velocity increases to conserve angular momentum ($L$ remains constant).

1. Identify the initial and final states. 2. Determine if any external torques are acting on the system. 3. If no external torques, set initial angular momentum equal to final angular momentum ($L_{initial} = L_{final}$). 4. Substitute appropriate formulas for angular momentum (e.g., $I\omega$). 5. Solve for the unknown variable.