A cyclist starts from rest and pedals so that the wheels make 8.00 revolutions in the first 7.40 s. What is the angular acceleration of the wheels (assumed constant)? rad/s2
A cyclist starts from rest and pedals so that the wheels make 8.00 revolutions in the first 7.40 s. What is the angular acceleration of the wheels (assumed constant)? rad/s2
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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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.
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![**Problem Description:**
A cyclist starts from rest and pedals so that the wheels make 8.00 revolutions in the first 7.40 seconds. What is the angular acceleration of the wheels (assumed constant)?
**Required:**
Calculate the angular acceleration in \(\text{rad/s}^2\).
**Solution Explanation:**
To find the angular acceleration, we first need to convert the number of revolutions into radians. Since one revolution is \(2\pi\) radians, 8.00 revolutions are:
\[ \theta = 8.00 \times 2\pi \, \text{radians} \]
Since the cyclist starts from rest, the initial angular velocity (\(\omega_0\)) is \(0 \, \text{rad/s}\).
Using the formula for angular displacement under constant angular acceleration:
\[ \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \]
Substituting the known values:
\[ 8.00 \times 2\pi = 0 \times 7.40 + \frac{1}{2} \alpha (7.40)^2 \]
Solve for angular acceleration \(\alpha\):
\[ \alpha = \frac{2 \times 8.00 \times 2\pi}{(7.40)^2} \]
Calculate \(\alpha\) to find the angular acceleration in \(\text{rad/s}^2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fd20e11-2399-44a5-beb6-e921116d74ba%2F3feb46c0-d41f-47cb-9e6a-21145e5ab5b1%2Fq5sgo1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
A cyclist starts from rest and pedals so that the wheels make 8.00 revolutions in the first 7.40 seconds. What is the angular acceleration of the wheels (assumed constant)?
**Required:**
Calculate the angular acceleration in \(\text{rad/s}^2\).
**Solution Explanation:**
To find the angular acceleration, we first need to convert the number of revolutions into radians. Since one revolution is \(2\pi\) radians, 8.00 revolutions are:
\[ \theta = 8.00 \times 2\pi \, \text{radians} \]
Since the cyclist starts from rest, the initial angular velocity (\(\omega_0\)) is \(0 \, \text{rad/s}\).
Using the formula for angular displacement under constant angular acceleration:
\[ \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \]
Substituting the known values:
\[ 8.00 \times 2\pi = 0 \times 7.40 + \frac{1}{2} \alpha (7.40)^2 \]
Solve for angular acceleration \(\alpha\):
\[ \alpha = \frac{2 \times 8.00 \times 2\pi}{(7.40)^2} \]
Calculate \(\alpha\) to find the angular acceleration in \(\text{rad/s}^2\).
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