Angular Momentum Quiz with Answers for AP Physics 1

📚 Quick Study Guide

⚛️ Angular momentum ($L$) is a vector quantity representing the rotational momentum of an object. 🔄 For a point particle, $L = I\omega = r \times p = rmv\sin(\theta)$, where $r$ is the position vector, $p$ is the linear momentum, $m$ is mass, $v$ is velocity and $\theta$ is the angle between $r$ and $p$. 🎢 For a rigid body, $L = I\omega$, where $I$ is the moment of inertia and $\omega$ is the angular velocity. ⚖️ Conservation of Angular Momentum: If the net external torque acting on a system is zero, the total angular momentum of the system remains constant ($L_i = L_f$). 🔩 Torque ($\tau$) is the rate of change of angular momentum: $\tau = \frac{dL}{dt} = rF\sin(\theta)$, where $F$ is the force applied. 💫 Moment of Inertia ($I$) depends on the mass distribution and the axis of rotation (e.g., for a point mass, $I = mr^2$). 💡 Kinetic Energy of Rotation: $KE_{rot} = \frac{1}{2}I\omega^2$

🧪 Practice Quiz

1. A spinning skater pulls her arms in, decreasing her moment of inertia by a factor of 2. What happens to her angular speed?
   1. It remains the same.
   2. It decreases by a factor of 2.
   3. It increases by a factor of 2.
   4. It increases by a factor of 4.
2. A particle of mass $m$ moves with a constant speed $v$ along a straight line. What is the angular momentum of the particle with respect to a point O not on the line?
   1. Zero
   2. $mvr$, where $r$ is the perpendicular distance from O to the line
   3. $mv$
   4. Infinite
3. A rotating wheel has an initial angular momentum of $5 kg \cdot m^2/s$. A constant torque of $2 N \cdot m$ is applied to it, opposing its rotation. How long will it take for the wheel to come to a stop?
   1. 2.5 s
   2. 5 s
   3. 10 s
   4. 20 s
4. A solid sphere and a hollow sphere have the same mass and radius. Which one has a larger moment of inertia about an axis through its center?
   1. Solid sphere
   2. Hollow sphere
   3. They have the same moment of inertia.
   4. It depends on their density.
5. A student sits on a rotating stool holding a spinning bicycle wheel. If the student turns the wheel over so that it spins in the opposite direction, what happens?
   1. The student starts rotating in the same direction.
   2. The student starts rotating in the opposite direction.
   3. The student does not rotate.
   4. The wheel stops spinning.
6. A uniform rod of length $L$ and mass $M$ is pivoted at one end. What is the moment of inertia of the rod about this pivot point?
   1. $\frac{1}{12}ML^2$
   2. $\frac{1}{3}ML^2$
   3. $\frac{1}{2}ML^2$
   4. $ML^2$
7. Two identical disks are rotating about the same axis. Disk A has twice the angular speed of Disk B. The ratio of the angular momentum of Disk A to Disk B is:
   1. 1:1
   2. 1:2
   3. 2:1
   4. 4:1