Torque as the Rate of Change of Angular Momentum Quiz with Answers

📚 Quick Study Guide

• 📏 Torque Defined: 🔄 Torque ($\tau$) is the rotational equivalent of force. It causes an object to rotate.
• 🧮 Formula: The magnitude of torque is given by $\tau = rF\sin(\theta)$, 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.
• ⚛️ Angular Momentum: Angular momentum ($L$) is a measure of an object's rotation. For a point mass, $L = I\omega$, where $I$ is the moment of inertia and $\omega$ is the angular velocity.
• ⏱️ Rate of Change: Torque is the rate of change of angular momentum: $\tau = \frac{dL}{dt}$. This means that a net torque applied to an object will change its angular momentum over time.
• 🧭 Direction: Both torque and angular momentum are vector quantities, with directions determined by the right-hand rule.
• ⚖️ Conservation: In the absence of external torques, angular momentum is conserved.

Practice Quiz

1. What is the relationship between torque ($\tau$) and angular momentum ($L$)?
   1. $\tau = L$
   2. $\tau = \frac{dL}{dt}$
   3. $L = \frac{d\tau}{dt}$
   4. $\tau = \int L dt$
2. A spinning skater pulls their arms closer to their body. What happens to their angular momentum?
   1. Increases
   2. Decreases
   3. Remains constant
   4. Becomes zero
3. If the net torque on an object is zero, what can be said about its angular momentum?
   1. It is increasing.
   2. It is decreasing.
   3. It is constant.
   4. It is oscillating.
4. A force of 10 N is applied 0.5 m from the axis of rotation, at an angle of 90 degrees. What is the magnitude of the torque?
   1. 2 N⋅m
   2. 5 N⋅m
   3. 10 N⋅m
   4. 20 N⋅m
5. Which of the following is the correct unit for torque?
   1. Newton (N)
   2. Joule (J)
   3. Newton-meter (N⋅m)
   4. Watt (W)
6. What happens to the angular momentum of a spinning top as it slows down due to friction?
   1. Increases
   2. Decreases
   3. Remains constant
   4. Becomes infinite
7. If the angular momentum of a system is conserved, what does this imply about the net external torque on the system?
   1. It is positive.
   2. It is negative.
   3. It is zero.
   4. It is changing.