### Rotational Dynamics of a Double Ball System#### Diagram Description:The image depicts a horizontal rod with two balls attached at each end. The rod is positioned vertically on a pivot. The balls are rotating around the vertical axis, with an angular velocity \( v \). The system experiences a torque \( M \) and is annotated with the following expression:\[ M = (t^2 + 2) \, \text{N} \cdot \text{m} \]where \( t \) is the time in seconds. The distance from the pivot to each ball along the rod is \( 0.5 \, \text{m} \).#### Problem Description:- Each ball has a negligible size. Their respective masses are \( 7 \, \text{kg} \) and \( 3 \, \text{kg} \).- Each ball is attached to the end of a rod whose mass may be neglected.- If the rod is subjected to a torque \( M = t^2 + 4 \, \text{N} \cdot \text{m} \), where \( t \) is in seconds, determine the speed of each ball when \( t = 1 \).- The initial speed of each ball at \( t = 0 \, \text{s} \) is \( 1 \, \text{m/s} \).### Objective:Calculate the speed of each ball at \( t = 1 \, \text{s} \) given the conditions above.

Answered: Image /qna-images/answer/a5b9c1c8-907b-44ff-adb9-9213c4a8c4c4.jpg

Each ball has a negligible size and their respective mass are 7-kg and 3-kg. Each ball is attached to the end of a rod whose mass may be neglected. If the rod is subjected to a torque M-t²+4 N.m, where t is in seconds, detemrine the speed of each ball when t=1. The initial speed of each baal at t=0s is 1 m/s.

Each ball has a negligible size and their respective mass are 7-kg and 3-kg. Each ball is attached to the end of a rod whose mass may be neglected. If the rod is subjected to a torque M-t²+4 N.m, where t is in seconds, detemrine the speed of each ball when t=1. The initial speed of each baal at t=0s is 1 m/s.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

### Rotational Dynamics of a Double Ball System

#### Diagram Description:

The image depicts a horizontal rod with two balls attached at each end. The rod is positioned vertically on a pivot. The balls are rotating around the vertical axis, with an angular velocity \( v \). The system experiences a torque \( M \) and is annotated with the following expression:

\[ M = (t^2 + 2) \, \text{N} \cdot \text{m} \]

where \( t \) is the time in seconds. The distance from the pivot to each ball along the rod is \( 0.5 \, \text{m} \).

#### Problem Description:

- Each ball has a negligible size. Their respective masses are \( 7 \, \text{kg} \) and \( 3 \, \text{kg} \).
- Each ball is attached to the end of a rod whose mass may be neglected.
- If the rod is subjected to a torque \( M = t^2 + 4 \, \text{N} \cdot \text{m} \), where \( t \) is in seconds, determine the speed of each ball when \( t = 1 \).
- The initial speed of each ball at \( t = 0 \, \text{s} \) is \( 1 \, \text{m/s} \).

### Objective:

Calculate the speed of each ball at \( t = 1 \, \text{s} \) given the conditions above.

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