### Physics Problem: Wind Turbine Angular Acceleration#### Problem StatementA wind turbine is initially spinning at a constant angular speed. As the wind's strength gradually increases, the turbine experiences a constant angular acceleration of 0.176 rad/s². After making 2870 revolutions, its angular speed is 129 rad/s.**Questions:**(a) What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up?#### Solution StepsTo solve this problem, you'll need to use the equations of angular motion.---#### Input Fields for Calculation(a) **Initial Angular Velocity (ω₀)**- Input field for numerical value- Dropdown for units (e.g., rad/s)(b) **Time Elapsed (t)**- Input field for numerical value- Dropdown for units (e.g., seconds)---Please fill in the values for these quantities based on your calculations. Use the provided formulas for angular motion to derive the required values.**Note:** Ensure your answers include appropriate units for better clarity and accuracy.

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A wind turbine is initially spinning at a constant angular speed. As the wind's strength gradually increases, the turbine experiences a constant angular acceleration 0.176 rad/s². After making 2870 revolutions, its angular speed is 129 rad/s. (a) What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up? (a) Number i Units (b) Number i Units

A wind turbine is initially spinning at a constant angular speed. As the wind's strength gradually increases, the turbine experiences a constant angular acceleration 0.176 rad/s². After making 2870 revolutions, its angular speed is 129 rad/s. (a) What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up? (a) Number i Units (b) Number i Units

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

### Physics Problem: Wind Turbine Angular Acceleration

#### Problem Statement
A wind turbine is initially spinning at a constant angular speed. As the wind's strength gradually increases, the turbine experiences a constant angular acceleration of 0.176 rad/s². After making 2870 revolutions, its angular speed is 129 rad/s.

**Questions:**
(a) What is the initial angular velocity of the turbine?
(b) How much time elapses while the turbine is speeding up?

#### Solution Steps
To solve this problem, you'll need to use the equations of angular motion.

---

#### Input Fields for Calculation

(a) **Initial Angular Velocity (ω₀)**
- Input field for numerical value
- Dropdown for units (e.g., rad/s)

(b) **Time Elapsed (t)**
- Input field for numerical value
- Dropdown for units (e.g., seconds)

---

Please fill in the values for these quantities based on your calculations. Use the provided formulas for angular motion to derive the required values.

**Note:** Ensure your answers include appropriate units for better clarity and accuracy.

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