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A cylinder rolls without slipping between two moving plates C and D. The radius of the cylinder is r=4.0m. The velocity of the plate C is VC=6.0 m/s to the right. The velocity of the plate D is VD=2.0 m/s to the left. Using the instantaneous center of zero velocity (IC) to determine (1) The distance between point A and IC point, rA/IC=_____ m

A cylinder rolls without slipping between two moving plates C and D. The radius of the cylinder is r=4.0m. The velocity of the plate C is VC=6.0 m/s to the right. The velocity of the plate D is VD=2.0 m/s to the left. Using the instantaneous center of zero velocity (IC) to determine (1) The distance between point A and IC point, rA/IC=_____ m

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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A cylinder rolls without slipping between two moving plates C and D.  The radius of the cylinder is r=4.0m. The velocity of the plate C is  VC=6.0 m/s to the right. The velocity of the plate D is VD=2.0 m/s to the left. Using the instantaneous center of zero velocity (IC) to determine

 

(1) The distance between point A and IC point, rA/IC=_____ m



### Rolling Cylinder Between Two Moving Plates: Problem Analysis **Problem Statement:** A cylinder rolls without slipping between two moving plates, C and D. The radius of the cylinder is \( r = 4.0 \text{ m} \). The velocity of plate C is \( V_C = 6.0 \text{ m/s} \) to the right. The velocity of plate D is \( V_D = 2.0 \text{ m/s} \) to the left. Using the instantaneous center of zero velocity (IC), determine: 1. **The distance between point A and the IC (r_{A/IC}) in meters** **Diagram Explanation:** In the provided diagram, several key components are illustrated: - A large cylinder is depicted rolling between two horizontally moving plates: Plate C (above the cylinder) and Plate D (below the cylinder). - The cylinder has its radius labeled as r = 4.0 m. - Plate C is moving to the right with a velocity \( V_C = 6.0 \text{ m/s} \). - Plate D is moving to the left with a velocity \( V_D = 2.0 \text{ m/s} \). - The instantaneous center of zero velocity (IC) is marked on the diagram below the center point of the cylinder. **Key Points in the Diagram:** - **A**: Point on the circumference of the cylinder at the top (contact with plate C). - **B**: Point on the circumference of the cylinder at the bottom (contact with plate D). - **Center of Cylinder**: Located midway between points A and B. - **IC (Instantaneous Center)**: The point of zero velocity used to analyze the rotational motion of the cylinder. Red vertical arrow pointing from the center of the cylinder to point A denotes \( r_{A/IC} \). Blue vertical arrow from the center to the IC denotes \( r_{C/IC} \). ### Calculation of r_{A/IC} To determine the distance between point A and the IC (represented as \( r_{A/IC} \)), we need to apply the principle that the point on the circumference where the cylinder is in contact with the plates temporarily has zero velocity concerning the IC due to rolling without slipping. By applying the instantaneous center of zero velocity and using the relationship between angular velocity and linear velocity, we can derive: \[ V_A = V_C \text{
Transcribed Image Text:### Rolling Cylinder Between Two Moving Plates: Problem Analysis **Problem Statement:** A cylinder rolls without slipping between two moving plates, C and D. The radius of the cylinder is \( r = 4.0 \text{ m} \). The velocity of plate C is \( V_C = 6.0 \text{ m/s} \) to the right. The velocity of plate D is \( V_D = 2.0 \text{ m/s} \) to the left. Using the instantaneous center of zero velocity (IC), determine: 1. **The distance between point A and the IC (r_{A/IC}) in meters** **Diagram Explanation:** In the provided diagram, several key components are illustrated: - A large cylinder is depicted rolling between two horizontally moving plates: Plate C (above the cylinder) and Plate D (below the cylinder). - The cylinder has its radius labeled as r = 4.0 m. - Plate C is moving to the right with a velocity \( V_C = 6.0 \text{ m/s} \). - Plate D is moving to the left with a velocity \( V_D = 2.0 \text{ m/s} \). - The instantaneous center of zero velocity (IC) is marked on the diagram below the center point of the cylinder. **Key Points in the Diagram:** - **A**: Point on the circumference of the cylinder at the top (contact with plate C). - **B**: Point on the circumference of the cylinder at the bottom (contact with plate D). - **Center of Cylinder**: Located midway between points A and B. - **IC (Instantaneous Center)**: The point of zero velocity used to analyze the rotational motion of the cylinder. Red vertical arrow pointing from the center of the cylinder to point A denotes \( r_{A/IC} \). Blue vertical arrow from the center to the IC denotes \( r_{C/IC} \). ### Calculation of r_{A/IC} To determine the distance between point A and the IC (represented as \( r_{A/IC} \)), we need to apply the principle that the point on the circumference where the cylinder is in contact with the plates temporarily has zero velocity concerning the IC due to rolling without slipping. By applying the instantaneous center of zero velocity and using the relationship between angular velocity and linear velocity, we can derive: \[ V_A = V_C \text{
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