### Section: Rotational Dynamics with a Bicycle Wheel#### Introduction**Figure 1:**A bicycle wheel is mounted on a fixed, frictionless axle, with a light string wound around its rim. The wheel has moment of inertia \( I = kmr^2 \), where \( m \) is its mass, \( r \) is its radius, and \( k \) is a dimensionless constant between zero and one. The wheel is rotating counterclockwise with angular speed \( \omega_0 \), when at time \( t = 0 \) someone starts pulling the string with a force of magnitude \( F \). Assume that the string does not slip on the wheel.**Diagram:**- The figure shows a side view of the bicycle wheel.- The wheel is depicted with a string wrapped around its rim.- The string is shown being pulled horizontally with a force \( \vec{F} \).- The wheel is mounted vertically with its axle fixed in place, and it rotates counterclockwise.#### Problem Statement**Part A:**Suppose that after a certain time \( t_L \), the string has been pulled through a distance \( L \). What is the final rotational speed \( \omega_{\text{final}} \) of the wheel? Express your answer in terms of \( L, F, I, \) and \( \omega_0 \).\[ \omega_{\text{final}} = \]**Part B:**What is the instantaneous power \( P \) delivered to the wheel via the force \( \vec{F} \) at time \( t = 0 \)? Express the power in terms of some or all of the variables given in the problem introduction.\[ P = \]---This exercise explores the principles of rotational motion and the effect of torque and power on a rotating body.

Answered: Image /qna-images/answer/7c8a8473-d424-4617-a611-521bc50096bc.jpg

(Figure 1) A bicycle wheel is mounted on a fixed, frictionless axle, with a light string wound around its rim. The wheel has moment of inertia I = km2, where m is its mass, r is its radius, and k is a dimensionless constant between zero and one. The wheel is rotating counterclockwise with angular speed wo, when at time t=0 someone starts pulling the string with a force of magnitude F. Assume that the string does not slip on the wheel. Figure W < 1 of 1 > Suppose that after a certain time t, the string has been pulled through a distance L. What is the final rotational speed wfinal of the wheel? Express your answer in terms of L, F, I, and wo ▸ View Available Hint(s) Wfinal= Submit ▾ Part B P= 195) ΑΣΦ Submit a What is the instantaneous power P delivered to the wheel via the force F at time t = 0? Express the power in terms of some or all of the variables given in the problem introduction. ▸ View Available Hint(s) IVE ΑΣΦ ? ?

(Figure 1) A bicycle wheel is mounted on a fixed, frictionless axle, with a light string wound around its rim. The wheel has moment of inertia I = km2, where m is its mass, r is its radius, and k is a dimensionless constant between zero and one. The wheel is rotating counterclockwise with angular speed wo, when at time t=0 someone starts pulling the string with a force of magnitude F. Assume that the string does not slip on the wheel. Figure W < 1 of 1 > Suppose that after a certain time t, the string has been pulled through a distance L. What is the final rotational speed wfinal of the wheel? Express your answer in terms of L, F, I, and wo ▸ View Available Hint(s) Wfinal= Submit ▾ Part B P= 195) ΑΣΦ Submit a What is the instantaneous power P delivered to the wheel via the force F at time t = 0? Express the power in terms of some or all of the variables given in the problem introduction. ▸ View Available Hint(s) IVE ΑΣΦ ? ?

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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Question

### Section: Rotational Dynamics with a Bicycle Wheel

#### Introduction

**Figure 1:**
A bicycle wheel is mounted on a fixed, frictionless axle, with a light string wound around its rim. The wheel has moment of inertia \( I = kmr^2 \), where \( m \) is its mass, \( r \) is its radius, and \( k \) is a dimensionless constant between zero and one. The wheel is rotating counterclockwise with angular speed \( \omega_0 \), when at time \( t = 0 \) someone starts pulling the string with a force of magnitude \( F \). Assume that the string does not slip on the wheel.

**Diagram:**
- The figure shows a side view of the bicycle wheel.
- The wheel is depicted with a string wrapped around its rim.
- The string is shown being pulled horizontally with a force \( \vec{F} \).
- The wheel is mounted vertically with its axle fixed in place, and it rotates counterclockwise.

#### Problem Statement

**Part A:**
Suppose that after a certain time \( t_L \), the string has been pulled through a distance \( L \). What is the final rotational speed \( \omega_{\text{final}} \) of the wheel? Express your answer in terms of \( L, F, I, \) and \( \omega_0 \).

\[ \omega_{\text{final}} = \]

**Part B:**
What is the instantaneous power \( P \) delivered to the wheel via the force \( \vec{F} \) at time \( t = 0 \)? Express the power in terms of some or all of the variables given in the problem introduction.

\[ P = \]

---

This exercise explores the principles of rotational motion and the effect of torque and power on a rotating body.

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