### Problem StatementA person is riding a bicycle, and its wheels have an angular velocity of \( 14.0 \, \text{rad/s} \). Then, the brakes are applied, and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is \( 13.8 \) revolutions. 1. **(a)** How much time does it take for the bike to come to rest? - **Input Box**: Number [Units]2. **(b)** What is the angular acceleration (in \( \text{rad/s}^2 \)) of each wheel? - **Input Box**: Number [Units]### Detailed Explanation of ProblemThis problem deals with angular motion concepts such as angular velocity, angular displacement, and angular acceleration. Here are the steps to solve the problem:1. **Given Data**: - Initial angular velocity, \( \omega_0 = 14.0 \, \text{rad/s} \) - Angular displacement, \( \theta = 13.8 \) revolutions (convert this to radians if necessary, \( 1 \text{ revolution} = 2\pi \text{ radians} \))2. **Convert Angular Displacement to Radians**: \[ \theta (\text{radians}) = 13.8 \times 2\pi \]3. **Calculate Time to Come to Rest**: To find the time, \( t \), use the equation of motion for angular variables: \[ \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \] Here \( \omega = 0 \, \text{rad/s} \) at rest.4. **Calculate Angular Acceleration**: Use the equation involving initial angular velocity and time: \[ \omega = \omega_0 + \alpha t \] Given \( \omega = 0 \): \[ 0 = 14.0 + \alpha t \] Rearranging gives: \[ \alpha = -\frac{14.0}{t} \]### Solution Steps- Calculate the time \( t \) using the displacement equation.- Once \( t \) is found, calculate angular acceleration \( \alpha \

Given that, Angular velocity = 14.0rad/s Angular displacement of each wheel = 13.8 revolutions

A person is riding a bicycle, and its wheels have an angular velocity of 14.0 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 13.8 revolutions. (a) How much time does it take for the bike to come to rest? (b) What is the anguar acceleration (in rad/s2) of each wheel? (a) Number Units (b) Number Units

A person is riding a bicycle, and its wheels have an angular velocity of 14.0 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 13.8 revolutions. (a) How much time does it take for the bike to come to rest? (b) What is the anguar acceleration (in rad/s2) of each wheel? (a) Number Units (b) Number Units

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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