29 **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 \(\text{rad/s}^2\).

Given data: Initial angular velocity (ω0) = 0 rad/s Angular displacement (Δθ) = 8.00 revolutions…

Answered: A cyclist starts from rest and pedals…

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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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

**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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