During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 31.1 rad/s. Find the angular displacement A0 of the tub during a spin of 98.9 s, expressed both in radians and in revolutions.
During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 31.1 rad/s. Find the angular displacement A0 of the tub during a spin of 98.9 s, expressed both in radians and in revolutions.
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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![**Problem Description:**
During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 31.1 rad/s. Find the angular displacement \( \Delta \theta \) of the tub during a spin of 98.9 s, expressed both in radians and in revolutions.
**Solution:**
1. **Angular Displacement in Radians:**
\[
\Delta \theta = \text{Angular velocity} \times \text{Time} = 31.1 \, \text{rad/s} \times 98.9 \, \text{s}
\]
\[
\Delta \theta = \boxed{3073.79} \, \text{rad}
\]
2. **Angular Displacement in Revolutions:**
\[
\Delta \theta = \frac{3073.79 \, \text{rad}}{2\pi}
\]
\[
\Delta \theta = \boxed{489.35} \, \text{revolutions}
\]
*Note: In this context, one full revolution is equal to \(2\pi\) radians.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb8635a0-8b2a-40cb-87d0-b22d177615a6%2Fc88547c8-7ae9-4610-af4e-e1a636065775%2Fza4pdzd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 31.1 rad/s. Find the angular displacement \( \Delta \theta \) of the tub during a spin of 98.9 s, expressed both in radians and in revolutions.
**Solution:**
1. **Angular Displacement in Radians:**
\[
\Delta \theta = \text{Angular velocity} \times \text{Time} = 31.1 \, \text{rad/s} \times 98.9 \, \text{s}
\]
\[
\Delta \theta = \boxed{3073.79} \, \text{rad}
\]
2. **Angular Displacement in Revolutions:**
\[
\Delta \theta = \frac{3073.79 \, \text{rad}}{2\pi}
\]
\[
\Delta \theta = \boxed{489.35} \, \text{revolutions}
\]
*Note: In this context, one full revolution is equal to \(2\pi\) radians.*
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