# Spinning WheelOn the left are formulas for linear motion with constant acceleration. On the right, write down the corresponding formulas for angular motion with constant angular acceleration.| | Linear | Angular ||-----|-----------------|----------------------|| 1. | \( x(t) \) | \( \theta(t) \) || 2. | \( v = \frac{dx}{dt} \) | \( \omega = \frac{d\theta}{dt} \) || 3. | \( a = \frac{dv}{dt} = \frac{d^2x}{dt^2} = \text{const} \) | \( \alpha = \frac{d\omega}{dt} = \frac{d^2\theta}{dt^2} = \text{const} \) || 4. | \( v = v_0 + at \) | || 5. | \( x = x_0 + v_0t + \frac{1}{2}at^2 \) | || 6. | \( v^2 = v_0^2 + 2a\Delta x \) | || 7. | \( x = x_0 + \frac{1}{2}(v + v_0)t \) | |---**Use these equations to answer the following:**A wheel starts at rest and turns with angular acceleration of \( 1.88 \, \text{rad/s}^2 \). How long does it take to make 2 revolutions? What is its angular speed?

Given data: Initial angular velocity (ω0) = 0 rad/s Angular acceleration (α) = 1.88 rad/s2 Angular…

Answered: A wheel starts at rest and turns with…

A wheel starts at rest and turns with angular acceleration of 1.88 rad/s². How long does it take to make 2 revolutions? What is it's angular speed?

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

# Spinning Wheel

On the left are formulas for linear motion with constant acceleration. On the right, write down the corresponding formulas for angular motion with constant angular acceleration.

| | Linear | Angular |
|-----|-----------------|----------------------|
| 1. | \( x(t) \) | \( \theta(t) \) |
| 2. | \( v = \frac{dx}{dt} \) | \( \omega = \frac{d\theta}{dt} \) |
| 3. | \( a = \frac{dv}{dt} = \frac{d^2x}{dt^2} = \text{const} \) | \( \alpha = \frac{d\omega}{dt} = \frac{d^2\theta}{dt^2} = \text{const} \) |
| 4. | \( v = v_0 + at \) | |
| 5. | \( x = x_0 + v_0t + \frac{1}{2}at^2 \) | |
| 6. | \( v^2 = v_0^2 + 2a\Delta x \) | |
| 7. | \( x = x_0 + \frac{1}{2}(v + v_0)t \) | |

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**Use these equations to answer the following:**

A wheel starts at rest and turns with angular acceleration of \( 1.88 \, \text{rad/s}^2 \). How long does it take to make 2 revolutions? What is its angular speed?

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