Examples of Torque and Angular Momentum Change in Real Life

📚 Quick Study Guide

• 🍎 Torque ($\tau$): The rotational equivalent of force. It causes an object to rotate. Formula: $\tau = rF\sin(\theta)$, where $r$ is the distance from the axis of rotation, $F$ is the force, and $\theta$ is the angle between $r$ and $F$.
• 🔄 Angular Momentum ($L$): A measure of an object's rotation. Formula: $L = I\omega$, where $I$ is the moment of inertia and $\omega$ is the angular velocity.
• 🎢 Change in Angular Momentum: Occurs when there is a net torque acting on a system. $\Delta L = \tau \Delta t$
• ⛸️ Conservation of Angular Momentum: In a closed system, the total angular momentum remains constant if no external torque acts on it.
• ⏱️ Real-world Examples: Include spinning tops, ice skaters changing their spin rate, and tightening bolts with a wrench.

Practice Quiz

1. Which of the following is the correct formula for torque?
   1. A. $\tau = rF\cos(\theta)$
   2. B. $\tau = rF\sin(\theta)$
   3. C. $\tau = F/r$
   4. D. $\tau = mr^2$
2. An ice skater spins faster when they pull their arms closer to their body. This is an example of:
   1. A. Increasing torque
   2. B. Decreasing angular momentum
   3. C. Conservation of angular momentum
   4. D. Increasing moment of inertia
3. What happens to the angular momentum of a spinning object if no external torque acts on it?
   1. A. It increases
   2. B. It decreases
   3. C. It remains constant
   4. D. It becomes zero
4. Tightening a bolt with a wrench involves applying:
   1. A. Linear momentum
   2. B. Angular velocity
   3. C. Torque
   4. D. Inertia
5. A spinning top slows down due to:
   1. A. Conservation of angular momentum
   2. B. Applied torque from friction
   3. C. Increased moment of inertia
   4. D. Decreased angular velocity
6. Which quantity is defined as the product of moment of inertia and angular velocity?
   1. A. Torque
   2. B. Angular momentum
   3. C. Force
   4. D. Linear momentum
7. If the net torque on an object is zero, what can you say about its angular momentum?
   1. A. It must be zero.
   2. B. It is changing.
   3. C. It is constant.
   4. D. It is increasing exponentially.