Real-world examples of positive and negative angular displacement

📚 Quick Study Guide

• 📐 Angular displacement is the change in the angle of an object. It's a vector quantity, meaning it has both magnitude and direction.
• ➕ A positive angular displacement indicates counter-clockwise rotation.
• ➖ A negative angular displacement indicates clockwise rotation.
• 🧭 The standard unit for angular displacement is radians (rad).
• 🔄 Angular displacement can be calculated using the formula: $ \theta = \frac{\text{arc length}}{\text{radius}} $
• 💡 Remember to consider the reference point when determining the direction of rotation.

Practice Quiz

1. A steering wheel is turned 90 degrees to the right. What is the angular displacement?

   1. $+\frac{\pi}{2}$ rad
   2. $-\frac{\pi}{2}$ rad
   3. $+\pi$ rad
   4. $-\pi$ rad

2. A door is opened a quarter of a full rotation in the counter-clockwise direction. What is the angular displacement?

   1. $-\frac{\pi}{2}$ rad
   2. $+\frac{\pi}{4}$ rad
   3. $+\frac{\pi}{2}$ rad
   4. $-\frac{\pi}{4}$ rad

3. A ceiling fan blade rotates 180 degrees clockwise. What is the angular displacement?

   1. $+\pi$ rad
   2. $-\frac{\pi}{2}$ rad
   3. $-\pi$ rad
   4. $+\frac{\pi}{2}$ rad

4. A figure skater completes 3 full rotations in a counter-clockwise direction. What is the angular displacement?

   1. $-6\pi$ rad
   2. $+3\pi$ rad
   3. $+6\pi$ rad
   4. $-3\pi$ rad

5. A bicycle wheel rotates half a turn backwards. What is the angular displacement?

   1. $+\pi$ rad
   2. $-\frac{\pi}{4}$ rad
   3. $-\pi$ rad
   4. $+\frac{\pi}{2}$ rad

6. A gymnast performs a somersault, rotating 360 degrees forward. What is the angular displacement?

   1. $+\pi$ rad
   2. $-2\pi$ rad
   3. $+2\pi$ rad
   4. $-\pi$ rad

7. A wrench is used to tighten a bolt by rotating it 45 degrees clockwise. What is the angular displacement?

   1. $+\frac{\pi}{4}$ rad
   2. $-\frac{\pi}{4}$ rad
   3. $+\frac{\pi}{2}$ rad
   4. $-\frac{\pi}{2}$ rad