AP Physics 1 Questions on Newton's Second Law for Rotation with Answers

📚 Quick Study Guide

• 🔄 [Relevant Emoji] Newton's Second Law for Rotation: $\tau_{net} = I \alpha$, where $\tau_{net}$ is the net torque, $I$ is the moment of inertia, and $\alpha$ is the angular acceleration.
• 📏 [Relevant Emoji] Torque: $\tau = rF\sin(\theta)$, where $r$ is the distance from the axis of rotation to the point where the force is applied, $F$ is the magnitude of the force, and $\theta$ is the angle between the force vector and the lever arm.
• 🧱 [Relevant Emoji] Moment of Inertia (I): Represents the resistance of an object to changes in its rotational motion. Depends on the mass distribution relative to the axis of rotation. For a point mass, $I = mr^2$. Different shapes have different formulas (given on formula sheet).
• ⏱️ [Relevant Emoji] Angular Acceleration: $\alpha = \frac{\Delta \omega}{\Delta t}$, where $\omega$ is angular velocity and $t$ is time.
• 🔗 [Relevant Emoji] Relationship between linear and angular quantities: $v = r\omega$, $a = r\alpha$.
• 📐 [Relevant Emoji] Work done by a torque: $W = \tau \Delta \theta$, where $\Delta \theta$ is the angular displacement.
• 💡 [Relevant Emoji] Remember to use consistent units (radians for angles!).

Practice Quiz

1. A wheel with a moment of inertia of $2.0 \text{ kg} \cdot \text{m}^2$ experiences a net torque of $10.0 \text{ N} \cdot \text{m}$. What is its angular acceleration?
   1. $2.0 \text{ rad/s}^2$
   2. $5.0 \text{ rad/s}^2$
   3. $12.0 \text{ rad/s}^2$
   4. $20.0 \text{ rad/s}^2$
2. A force of $20 \text{ N}$ is applied tangentially to the edge of a wheel with a radius of $0.5 \text{ m}$. What is the torque produced by this force?
   1. $5 \text{ N} \cdot \text{m}$
   2. $10 \text{ N} \cdot \text{m}$
   3. $20 \text{ N} \cdot \text{m}$
   4. $40 \text{ N} \cdot \text{m}$
3. A solid cylinder and a hollow cylinder have the same mass and radius. Which has a larger moment of inertia?
   1. Solid cylinder
   2. Hollow cylinder
   3. They have the same moment of inertia
   4. It depends on the height of the cylinders
4. An object's angular velocity increases from $2 \text{ rad/s}$ to $8 \text{ rad/s}$ in $3 \text{ s}$. If its moment of inertia is $3 \text{ kg} \cdot \text{m}^2$, what is the net torque acting on it?
   1. $2 \text{ N} \cdot \text{m}$
   2. $6 \text{ N} \cdot \text{m}$
   3. $8 \text{ N} \cdot \text{m}$
   4. $18 \text{ N} \cdot \text{m}$
5. A door requires a torque of $5 \text{ N} \cdot \text{m}$ to open. If you apply a force of $10 \text{ N}$ at a distance of $x$ meters from the hinges, what is the minimum value of $x$ to open the door effectively?
   1. $0.25 \text{ m}$
   2. $0.5 \text{ m}$
   3. $1.0 \text{ m}$
   4. $2.0 \text{ m}$
6. If the net torque on an object is zero, what can be said about its angular velocity?
   1. It must be zero.
   2. It must be constant.
   3. It must be increasing.
   4. It must be decreasing.
7. A rotating object has an angular momentum of $20 \text{ kg} \cdot \text{m}^2/\text{s}$ and a moment of inertia of $4 \text{ kg} \cdot \text{m}^2$. What is its angular velocity?
   1. $4 \text{ rad/s}$
   2. $5 \text{ rad/s}$
   3. $8 \text{ rad/s}$
   4. $10 \text{ rad/s}$