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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 (4) The magnitude of the velocity of the point O, VO=_________m/s

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 (4) The magnitude of the velocity of the point O, VO=_________m/s

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
Problem 1.1MA
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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

 

(4) The magnitude of the velocity of the point O, VO=_________m/s




 
 
 
 

## 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 the plate C is \( V_C = 6.0 \, \text{m/s} \) to the right. The velocity of the plate D is \( V_D = 2.0 \, \text{m/s} \) to the left. Using the instantaneous center of zero velocity (IC) to determine: (4) The magnitude of the velocity of the point O, \( V_O = \, \underline{\hspace{2cm}}\, \text{m/s} \) ### Diagram Explanation: The diagram consists of a cylinder in contact with two plates, labeled C and D. - Plate C is moving to the right with a velocity \( V_C \). - Plate D is moving to the left with a velocity \( V_D \). The cylinder is placed between the two plates and rolls without slipping. Several points are marked on the diagram: - Points A and B are the points of contact between the cylinder and the plates. - Point O is at the center of the cylinder. - The IC (Instantaneous Center of Zero Velocity) is located below the cylinder and to the left. ### Key Concepts: 1. **Instantaneous Center of Zero Velocity (IC):** This is a point on a rigid body where the velocity is momentarily zero. For rolling motion, the IC is useful in analyzing velocities at different points on the body. 2. **Rolling Without Slipping:** This means the point of contact with the surface (in this case, plates C and D) has zero relative velocity with respect to the surface. 3. **Velocity Relationship:** \[ V_A = V_C + V_{A/O} \] \[ V_B = V_D - V_{B/O} \] 4. **Relative Velocity (Between Points on the Cylinder):** \[ V_{A/O} = r \cdot \omega \] \[ V_{B/O} = r \cdot \omega \] Where \( \omega \) is the angular velocity of the cylinder. Using these principles, the problem requires the determination of the magnitude of the velocity of point O on the cylinder.
Transcribed Image Text:## 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 the plate C is \( V_C = 6.0 \, \text{m/s} \) to the right. The velocity of the plate D is \( V_D = 2.0 \, \text{m/s} \) to the left. Using the instantaneous center of zero velocity (IC) to determine: (4) The magnitude of the velocity of the point O, \( V_O = \, \underline{\hspace{2cm}}\, \text{m/s} \) ### Diagram Explanation: The diagram consists of a cylinder in contact with two plates, labeled C and D. - Plate C is moving to the right with a velocity \( V_C \). - Plate D is moving to the left with a velocity \( V_D \). The cylinder is placed between the two plates and rolls without slipping. Several points are marked on the diagram: - Points A and B are the points of contact between the cylinder and the plates. - Point O is at the center of the cylinder. - The IC (Instantaneous Center of Zero Velocity) is located below the cylinder and to the left. ### Key Concepts: 1. **Instantaneous Center of Zero Velocity (IC):** This is a point on a rigid body where the velocity is momentarily zero. For rolling motion, the IC is useful in analyzing velocities at different points on the body. 2. **Rolling Without Slipping:** This means the point of contact with the surface (in this case, plates C and D) has zero relative velocity with respect to the surface. 3. **Velocity Relationship:** \[ V_A = V_C + V_{A/O} \] \[ V_B = V_D - V_{B/O} \] 4. **Relative Velocity (Between Points on the Cylinder):** \[ V_{A/O} = r \cdot \omega \] \[ V_{B/O} = r \cdot \omega \] Where \( \omega \) is the angular velocity of the cylinder. Using these principles, the problem requires the determination of the magnitude of the velocity of point O on the cylinder.
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