**Physics Problem: Calculating Time for Angular Acceleration****Problem Statement:**An automatic dryer spins wet clothes at an angular speed of 5.6 rad/s. Starting from rest, the dryer reaches its operating speed with an average angular acceleration of 3.5 rad/s². How long does it take the dryer to come up to speed?**Solution Explanation:**To solve this problem, you can use the following kinematic equation for angular motion:\[ \omega_f = \omega_i + \alpha \cdot t \]where:- \( \omega_f \) is the final angular speed (5.6 rad/s),- \( \omega_i \) is the initial angular speed (0 rad/s, since it starts from rest),- \( \alpha \) is the angular acceleration (3.5 rad/s²),- \( t \) is the time taken to reach the final speed.Rearrange the formula to solve for \( t \):\[ t = \frac{\omega_f - \omega_i}{\alpha} \]Substitute the given values:\[ t = \frac{5.6 \, \text{rad/s} - 0 \, \text{rad/s}}{3.5 \, \text{rad/s}^2} \]Calculate the time \( t \).

Angular speed "wf"= 5.6rad/s . average angular acceleration"a"= 3.5 rad/s².

An automatic dryer spins wet clothes at an angular speed of 5.6 rad/s. Starting from rest, the dryer reaches its operating spe average angular acceleration of 3.5 rad/s². How long does it take the dryer to come up to speed? i

An automatic dryer spins wet clothes at an angular speed of 5.6 rad/s. Starting from rest, the dryer reaches its operating spe average angular acceleration of 3.5 rad/s². How long does it take the dryer to come up to speed? i

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: Calculating Time for Angular Acceleration**

**Problem Statement:**
An automatic dryer spins wet clothes at an angular speed of 5.6 rad/s. Starting from rest, the dryer reaches its operating speed with an average angular acceleration of 3.5 rad/s². How long does it take the dryer to come up to speed?

**Solution Explanation:**
To solve this problem, you can use the following kinematic equation for angular motion:

\[ \omega_f = \omega_i + \alpha \cdot t \]

where:
- \( \omega_f \) is the final angular speed (5.6 rad/s),
- \( \omega_i \) is the initial angular speed (0 rad/s, since it starts from rest),
- \( \alpha \) is the angular acceleration (3.5 rad/s²),
- \( t \) is the time taken to reach the final speed.

Rearrange the formula to solve for \( t \):

\[ t = \frac{\omega_f - \omega_i}{\alpha} \]

Substitute the given values:

\[ t = \frac{5.6 \, \text{rad/s} - 0 \, \text{rad/s}}{3.5 \, \text{rad/s}^2} \]

Calculate the time \( t \).

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