Torque Quiz with Answers: Test Your AP Physics C Knowledge

📚 Quick Study Guide

• 📐 Definition: Torque ($\tau$) is a twisting force that tends to cause rotation.
• 🧮 Formula: $\tau = rF\sin(\theta)$, 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 and the lever arm.
• ➕ Vector Nature: Torque is a vector quantity. The direction of the torque vector is perpendicular to both the force and the lever arm, determined by the right-hand rule.
• 🔄 Rotational Equilibrium: For an object to be in rotational equilibrium, the net torque acting on it must be zero ($\sum \tau = 0$).
• Moment of Inertia: The moment of inertia ($I$) is a measure of an object's resistance to rotational acceleration. For a point mass: $I = mr^2$. For complex shapes, $I$ can be calculated using integral calculus or looked up in tables.
• ⚖️ Newton's Second Law for Rotation: $\tau = I\alpha$, where $\alpha$ is the angular acceleration.
• 💪 Work Done by Torque: $W = \tau \theta$, where $\theta$ is the angular displacement.

Practice Quiz

1. What is the SI unit of torque?
   1. Newton (N)
   2. Joule (J)
   3. Newton-meter (N·m)
   4. Watt (W)
2. A force of 20 N is applied at a distance of 0.5 m from the axis of rotation, at an angle of 30 degrees. What is the magnitude of the torque?
   1. 5 N·m
   2. 10 N·m
   3. 17.3 N·m
   4. 20 N·m
3. For an object to be in rotational equilibrium, what condition must be met?
   1. The net force must be zero.
   2. The net torque must be zero.
   3. Both the net force and net torque must be zero.
   4. The object must be at rest.
4. What is the formula for the moment of inertia of a point mass $m$ at a distance $r$ from the axis of rotation?
   1. $I = mr$
   2. $I = \frac{1}{2}mr^2$
   3. $I = mr^2$
   4. $I = \frac{1}{2}mr$
5. A torque of 10 N·m is applied to an object with a moment of inertia of 2 kg·m². What is the angular acceleration of the object?
   1. 2 rad/s²
   2. 5 rad/s²
   3. 10 rad/s²
   4. 20 rad/s²
6. What is the work done by a torque of 5 N·m acting through an angle of 2 radians?
   1. 2.5 J
   2. 5 J
   3. 10 J
   4. 20 J
7. If the angle between the force vector and the lever arm is 0 degrees, what is the torque?
   1. Maximum
   2. Minimum (Zero)
   3. Equal to the force
   4. Equal to the lever arm