### 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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