### Problem Statement:**(a)** In the figure below, wheel A of radius \( r_A = 10 \, \text{cm} \) is coupled by belt B to wheel C of radius \( r_C = 25 \, \text{cm} \). The angular speed of wheel A is increased from rest at a constant rate of \( 1.6 \, \text{rad/s}^2 \). Find the time needed for wheel C to reach an angular speed of \( 100 \, \text{rev/min} \), assuming the belt does not slip. *(Hint: If the belt does not slip, the linear speeds at the two rims must be equal.)*### Explanation of the Diagram:The diagram shows two wheels, labeled A and C, connected by a belt, labeled B. The radius of wheel A (\( r_A \)) is 10 cm, and the radius of wheel C (\( r_C \)) is 25 cm. The belt B connects the two wheels such that if wheel A rotates, it transmits motion to wheel C via the belt. The connection via the belt implies that the tangential (linear) speed at the rim of wheel A is equal to the tangential speed at the rim of wheel C, assuming the belt does not slip.### Detailed Explanation:- **Given:** - Radius of wheel A, \( r_A = 10 \, \text{cm} = 0.1 \, \text{m} \) - Radius of wheel C, \( r_C = 25 \, \text{cm} = 0.25 \, \text{m} \) - Angular acceleration of wheel A, \( \alpha_A = 1.6 \, \text{rad/s}^2 \) - Target angular speed of wheel C, \( \omega_C = 100 \, \text{rev/min} = \frac{100 \times 2\pi}{60} \, \text{rad/s} = \frac{10\pi}{3} \, \text{rad/s} \)- **Find:** - Time \( t \) needed for wheel C to reach \( \omega_C = \frac{10\pi}{3} \, \text{rad/s} \)- **Solution Outline:** 1. Determine the relationship between the tangential speeds

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(a) In the figure below, wheel A of radius rA = 10 cm is co = B to wheel C of radius rc 25 cm. The angular s A is increased from rest at a constant rate of 1.6 rad time needed for wheel C to reach an angular speed of assuming the belt does not slip. (Hint: If the belt doe linear speeds at the two rims must be equal.) TC C B

(a) In the figure below, wheel A of radius rA = 10 cm is co = B to wheel C of radius rc 25 cm. The angular s A is increased from rest at a constant rate of 1.6 rad time needed for wheel C to reach an angular speed of assuming the belt does not slip. (Hint: If the belt doe linear speeds at the two rims must be equal.) TC C B

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 Statement:

**(a)** In the figure below, wheel A of radius \( r_A = 10 \, \text{cm} \) is coupled by belt B to wheel C of radius \( r_C = 25 \, \text{cm} \). The angular speed of wheel A is increased from rest at a constant rate of \( 1.6 \, \text{rad/s}^2 \). Find the time needed for wheel C to reach an angular speed of \( 100 \, \text{rev/min} \), assuming the belt does not slip. *(Hint: If the belt does not slip, the linear speeds at the two rims must be equal.)*

### Explanation of the Diagram:

The diagram shows two wheels, labeled A and C, connected by a belt, labeled B. The radius of wheel A (\( r_A \)) is 10 cm, and the radius of wheel C (\( r_C \)) is 25 cm. The belt B connects the two wheels such that if wheel A rotates, it transmits motion to wheel C via the belt. The connection via the belt implies that the tangential (linear) speed at the rim of wheel A is equal to the tangential speed at the rim of wheel C, assuming the belt does not slip.

### Detailed Explanation:

- **Given:**
- Radius of wheel A, \( r_A = 10 \, \text{cm} = 0.1 \, \text{m} \)
- Radius of wheel C, \( r_C = 25 \, \text{cm} = 0.25 \, \text{m} \)
- Angular acceleration of wheel A, \( \alpha_A = 1.6 \, \text{rad/s}^2 \)
- Target angular speed of wheel C, \( \omega_C = 100 \, \text{rev/min} = \frac{100 \times 2\pi}{60} \, \text{rad/s} = \frac{10\pi}{3} \, \text{rad/s} \)

- **Find:**
- Time \( t \) needed for wheel C to reach \( \omega_C = \frac{10\pi}{3} \, \text{rad/s} \)

- **Solution Outline:**
1. Determine the relationship between the tangential speeds

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