I need answer for 7,8,9 please follow the rules in first page ### Circular Motion and Rotational Dynamics Worksheet#### Key Formulas:- **Arc length formula**: \( s = r\theta \)- **Area of a sector formula**: \( A = \frac{1}{2} r^2 \theta \)- **Angular velocity**: \( \omega = \frac{\theta}{t} \)- **Linear velocity**: \( v = r\omega \)---1. **Problem:** Saint Petersburg, Russia and Alexandria, Egypt lie approximately on the same meridian. Saint Petersburg has a latitude of 60° N and Alexandria 32° N. Find the distance (in whole miles) between these two cities if the radius of the earth is about 3960 miles. **Solution:** Distance: ___________________________________________---2. **Problem:** Sprinkler heads come in assorted sizes depending on the angle of rotation desired. If a sprinkler head rotates 115° and has the pressure to keep a constant 14.5-foot spray, what is the area of the sector of the lawn that gets water? Round to the nearest square foot. **Solution:** Area: _______________________________________________---3. **Problem:** A lighthouse in the middle of a channel rotates its light in a circular motion with constant velocity. If the beacon of light completes one rotation every 8.5 seconds, what is the exact angular velocity of the beacon in radians per minute? **Solution:** Angular velocity: ____________________________________---4. **Problem:** Consider two gears working together (in a pulley-like situation) such that the smaller gear has a radius of 10 cm, while the larger gear has a radius of 26 cm. Find the radian measure rotation of the smaller gear when the large gear makes three complete rotations. **Solution:** Radian measure: _____________________________________---5. **Problem:** Each tire on a car has a diameter of 16.5 inches. The tires are rotating at 460 revolutions per minute. Find the speed of the automobile to the nearest mile per hour. Use dimensional analysis in steps when you show your work. **Solution:** Speed: _______________________________________________---**Note: Ensure your work is neat and organized, showing all formulas and step-by-step conversions as needed. Clearly write your simplified answers on the lines provided **Problem Set on Rotational Motion**This problem set focuses on the principles of rotational motion. Solve the following problems using appropriate formulae and steps. Carefully note down your process and round your final answers as directed.6. **Wind Machine Blade Speed Calculation** A wind machine used to generate electricity has blades that are 28 ft in length. The propeller is rotating at 4 revolutions per second. Find the linear speed of the tips of the blades in ft/min. \[ \text{Answer: } \underline{\hspace{100pt}} \]7. **Windshield Wiper Path Length** If a windshield wiper with a rubber part that is 17.5 inches long (blade and arm) rotates 158°, then what is the length of the path that the tip of the blade and the arm makes to the nearest tenth of an inch? \[ \text{Answer: } \underline{\hspace{100pt}} \]8. **Bicyclist Speed Calculation** How fast is a bicyclist traveling in miles per hour if his tires are 16 inches in diameter and the tire makes 2.75 revolutions per second? Use dimensional analysis in steps when you show your work. (Round to the nearest whole number) \[ \text{Answer: } \underline{\hspace{100pt}} \]9. **Grandfather Clock Pendulum Distance** The pendulum on a grandfather clock swings from side to side once every second. The length of the pendulum is 4.5 feet, and the angle through which it swings is 20°. Find the total distance traveled by the tip of the pendulum on the grandfather clock in one minute. \[ \text{Answer: } \underline{\hspace{100pt}} \]Students are encouraged to review the concepts of angular velocity, linear velocity, and dimensional analysis, ensuring thorough understanding and accurate calculations.

Answered: Image /qna-images/answer/10c49b0d-851e-4f3b-9fc7-1280f1595b9c.jpg

7. If a windshield wiper with a rubber part that is 17.5 inches long (blade and arm) rotates 158°, then what is the length of the path that the tip of the blade and the arm makes to the nearest tenth of an inch? 7. 8. How fast is a bicyclist traveling in miles per hour if his tires are 16 inches in diameter and the tire makes 2.75 revolutions per second? Use dimensional analysis in steps when you show your work. (Round to the nearest whole number) 8. 9. The pendulum on a grandfather clock swings from side to side once every second. The length of the pendulum is 4.5 feet, and the angle through which it swings is 20°. Find the total distance traveled by the tip of the pendulum on the grandfather clock in one minute.

7. If a windshield wiper with a rubber part that is 17.5 inches long (blade and arm) rotates 158°, then what is the length of the path that the tip of the blade and the arm makes to the nearest tenth of an inch? 7. 8. How fast is a bicyclist traveling in miles per hour if his tires are 16 inches in diameter and the tire makes 2.75 revolutions per second? Use dimensional analysis in steps when you show your work. (Round to the nearest whole number) 8. 9. The pendulum on a grandfather clock swings from side to side once every second. The length of the pendulum is 4.5 feet, and the angle through which it swings is 20°. Find the total distance traveled by the tip of the pendulum on the grandfather clock in one minute.

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter3: Radian Measure

Section3.5: Velocities

Problem 54PS: Velocity of a Ferris Wheel Use Figure 7 as a model of the Ferris wheel called Colossus that is built...

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I need answer for 7,8,9 please follow the rules in first page

### Circular Motion and Rotational Dynamics Worksheet

#### Key Formulas:
- **Arc length formula**: \( s = r\theta \)
- **Area of a sector formula**: \( A = \frac{1}{2} r^2 \theta \)
- **Angular velocity**: \( \omega = \frac{\theta}{t} \)
- **Linear velocity**: \( v = r\omega \)

---

1. **Problem:**
Saint Petersburg, Russia and Alexandria, Egypt lie approximately on the same meridian. Saint Petersburg has a latitude of 60° N and Alexandria 32° N. Find the distance (in whole miles) between these two cities if the radius of the earth is about 3960 miles.

**Solution:**

Distance: ___________________________________________

---

2. **Problem:**
Sprinkler heads come in assorted sizes depending on the angle of rotation desired. If a sprinkler head rotates 115° and has the pressure to keep a constant 14.5-foot spray, what is the area of the sector of the lawn that gets water? Round to the nearest square foot.

**Solution:**

Area: _______________________________________________

---

3. **Problem:**
A lighthouse in the middle of a channel rotates its light in a circular motion with constant velocity. If the beacon of light completes one rotation every 8.5 seconds, what is the exact angular velocity of the beacon in radians per minute?

**Solution:**

Angular velocity: ____________________________________

---

4. **Problem:**
Consider two gears working together (in a pulley-like situation) such that the smaller gear has a radius of 10 cm, while the larger gear has a radius of 26 cm. Find the radian measure rotation of the smaller gear when the large gear makes three complete rotations.

**Solution:**

Radian measure: _____________________________________

---

5. **Problem:**
Each tire on a car has a diameter of 16.5 inches. The tires are rotating at 460 revolutions per minute. Find the speed of the automobile to the nearest mile per hour. Use dimensional analysis in steps when you show your work.

**Solution:**

Speed: _______________________________________________

---

**Note: Ensure your work is neat and organized, showing all formulas and step-by-step conversions as needed. Clearly write your simplified answers on the lines provided

**Problem Set on Rotational Motion**

This problem set focuses on the principles of rotational motion. Solve the following problems using appropriate formulae and steps. Carefully note down your process and round your final answers as directed.

6. **Wind Machine Blade Speed Calculation**
A wind machine used to generate electricity has blades that are 28 ft in length. The propeller is rotating at 4 revolutions per second. Find the linear speed of the tips of the blades in ft/min.

\[ \text{Answer: } \underline{\hspace{100pt}} \]

7. **Windshield Wiper Path Length**
If a windshield wiper with a rubber part that is 17.5 inches long (blade and arm) rotates 158°, then what is the length of the path that the tip of the blade and the arm makes to the nearest tenth of an inch?

\[ \text{Answer: } \underline{\hspace{100pt}} \]

8. **Bicyclist Speed Calculation**
How fast is a bicyclist traveling in miles per hour if his tires are 16 inches in diameter and the tire makes 2.75 revolutions per second? Use dimensional analysis in steps when you show your work. (Round to the nearest whole number)

\[ \text{Answer: } \underline{\hspace{100pt}} \]

9. **Grandfather Clock Pendulum Distance**
The pendulum on a grandfather clock swings from side to side once every second. The length of the pendulum is 4.5 feet, and the angle through which it swings is 20°. Find the total distance traveled by the tip of the pendulum on the grandfather clock in one minute.

\[ \text{Answer: } \underline{\hspace{100pt}} \]

Students are encouraged to review the concepts of angular velocity, linear velocity, and dimensional analysis, ensuring thorough understanding and accurate calculations.

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