### Rotational Dynamics: Connected Wheels SystemIn the figure below, two wheels A and B have radii \( r_A = 31.0 \, \text{cm} \) and \( r_B = 14.0 \, \text{cm} \) respectively, and they are connected by a belt.![Connected Wheels](image_url)If wheel A accelerates uniformly from rest at \( 2.70 \, \text{rad/s}^2 \), determine the angular speed of wheel B after \( 8.40 \, \text{s} \), assuming the wheels rotate without slipping.**Explanation of the Figure:**- The figure depicts two wheels labeled A and B.- Wheel A has a radius of 31.0 cm, and wheel B has a radius of 14.0 cm.- The wheels are connected via a belt, ensuring that their tangential velocities are equal. This setup implies the wheels rotate without slipping.**Problem Solution:**To solve for the angular speed of wheel B after 8.40 seconds, follow these steps:1. **Define the Relationship Between the Angular Velocities:**Since the wheels are connected by a belt that does not slip, the tangential speed at the rims of wheels A and B will be the same:\[ v_A = v_B \]The tangential speed \( v \) is related to the angular speed \( \omega \) by the equation:\[ v = r \omega \]Therefore,\[ r_A \omega_A = r_B \omega_B \]2. **Find the Angular Speed of Wheel A:**Using the angular acceleration and the time given, we can find the angular speed of wheel A after 8.40 seconds. The angular speed \( \omega_A \) is given by:\[ \omega_A = \alpha t \]where \( \alpha \) is the angular acceleration and \( t \) is the time.Given \( \alpha = 2.70 \, \text{rad/s}^2 \) and \( t = 8.40 \, \text{s} \):\[ \omega_A = 2.70 \, \text{rad/s}^2 \times 8.40 \, \text{s} = 22.68 \, \text{rad/s} \]3. **Find the Angular Speed of Wheel B:**Using the relationship between

In the given question, Radius of wheel A = rA = 31.0cm = 0.31m Radius of wheel B = rB = 14cm =…

In the figure below, two wheels A and B of radii rA=31.0 cm and rg=14.0 cm respectively are connected by a belt. A B If A accelerates uniformly from rest at 2.70 rad/s², find the angular speed of B after 8.40 s, assuming the wheels rotate without slipping.

In the figure below, two wheels A and B of radii rA=31.0 cm and rg=14.0 cm respectively are connected by a belt. A B If A accelerates uniformly from rest at 2.70 rad/s², find the angular speed of B after 8.40 s, assuming the wheels rotate without slipping.

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

### Rotational Dynamics: Connected Wheels System

In the figure below, two wheels A and B have radii \( r_A = 31.0 \, \text{cm} \) and \( r_B = 14.0 \, \text{cm} \) respectively, and they are connected by a belt.

![Connected Wheels](image_url)

If wheel A accelerates uniformly from rest at \( 2.70 \, \text{rad/s}^2 \), determine the angular speed of wheel B after \( 8.40 \, \text{s} \), assuming the wheels rotate without slipping.

**Explanation of the Figure:**
- The figure depicts two wheels labeled A and B.
- Wheel A has a radius of 31.0 cm, and wheel B has a radius of 14.0 cm.
- The wheels are connected via a belt, ensuring that their tangential velocities are equal. This setup implies the wheels rotate without slipping.

**Problem Solution:**

To solve for the angular speed of wheel B after 8.40 seconds, follow these steps:

1. **Define the Relationship Between the Angular Velocities:**

Since the wheels are connected by a belt that does not slip, the tangential speed at the rims of wheels A and B will be the same:

\[ v_A = v_B \]

The tangential speed \( v \) is related to the angular speed \( \omega \) by the equation:

\[ v = r \omega \]

Therefore,

\[ r_A \omega_A = r_B \omega_B \]

2. **Find the Angular Speed of Wheel A:**

Using the angular acceleration and the time given, we can find the angular speed of wheel A after 8.40 seconds. The angular speed \( \omega_A \) is given by:

\[ \omega_A = \alpha t \]

where \( \alpha \) is the angular acceleration and \( t \) is the time.

Given \( \alpha = 2.70 \, \text{rad/s}^2 \) and \( t = 8.40 \, \text{s} \):

\[ \omega_A = 2.70 \, \text{rad/s}^2 \times 8.40 \, \text{s} = 22.68 \, \text{rad/s} \]

3. **Find the Angular Speed of Wheel B:**

Using the relationship between

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