AP Physics Questions on Conservation of Angular Momentum: Multiple Choice

📚 Quick Study Guide

• 🌀 Angular Momentum (L): A measure of an object's rotation. $L = I\omega$, where $I$ is the moment of inertia and $\omega$ is the angular velocity.
• 🔄 Moment of Inertia (I): Resistance to rotational motion. Depends on mass distribution. For a point mass: $I = mr^2$.
• 🧮 Angular Velocity ($\omega$): Rate of change of angular displacement. Measured in rad/s.
• ⚖️ Conservation of Angular Momentum: In a closed system, total angular momentum remains constant if no external torque acts on it. $L_{initial} = L_{final}$
• ⏱️ When to Apply: Use when dealing with rotating objects, collisions involving rotation, or changes in moment of inertia.
• 💡 Key Formula: $I_1\omega_1 = I_2\omega_2$
• 🔑 Important Note: Angular momentum is a vector quantity; direction matters!

🧪 Practice Quiz

1. A figure skater spins faster when she pulls her arms inward. This is because:
   1. (A) Her moment of inertia increases.
   2. (B) Her angular momentum increases.
   3. (C) Her angular momentum is conserved.
   4. (D) An external torque is applied.
2. A rotating wheel has its moment of inertia doubled while its angular momentum remains constant. What happens to its angular velocity?
   1. (A) It doubles.
   2. (B) It quadruples.
   3. (C) It halves.
   4. (D) It remains the same.
3. Two identical disks are rotating about the same axis. Disk A has twice the angular velocity of Disk B. What is the ratio of the angular momentum of Disk A to Disk B?
   1. (A) 1:1
   2. (B) 1:2
   3. (C) 2:1
   4. (D) 4:1
4. A spinning object changes its shape, causing its moment of inertia to decrease by a factor of 3. What happens to its angular velocity?
   1. (A) It decreases by a factor of 3.
   2. (B) It remains the same.
   3. (C) It increases by a factor of 3.
   4. (D) It increases by a factor of 9.
5. A child runs towards the center of a rotating merry-go-round. What happens to the angular velocity of the merry-go-round?
   1. (A) It decreases.
   2. (B) It remains the same.
   3. (C) It increases.
   4. (D) It stops.
6. A particle of mass $m$ moves in a circle of radius $r$ with a speed $v$. What is its angular momentum about the center of the circle?
   1. (A) $mv$
   2. (B) $mr$
   3. (C) $mvr$
   4. (D) $v/r$
7. A system consists of two objects rotating about a common axis. If no external torque acts on the system, what quantity is conserved?
   1. (A) Kinetic energy.
   2. (B) Angular speed.
   3. (C) Moment of inertia.
   4. (D) Angular momentum.