**Problem Statement:**A disk with mass \( m \) and radius \( R \) is released from rest at a height \( h \) and rolls without slipping down a ramp. What is the velocity of the center of the disk when it reaches the bottom of the slope? *(Hint: Use the work-energy principle. At each instant the disk rotates around the contact point \( C \), thus the inertia used for rotational kinetic energy should be computed around point \( C \) not point \( G \).)***Diagram Explanation:**The diagram shows a ramp inclined to the horizontal. A disk is positioned at the top of the ramp. The disk has a center of mass at point \( G \) and a contact point with the ramp at \( C \). The radius of the disk is indicated as \( R \), and the height from which the disk is released is shown as \( h \). The forces acting on the disk due to gravity will cause it to roll down the ramp.

The disc rolls without slipping.Calculation of moment of inertia of disc about CThe disc rolls without slippingV is the velocity of center of disc, is angular velocity.Calculation of velocity of center of disc when it reaches bottom pointApplying conservation of energyThe velocity of the center of the disc at bottom is .

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A disk with mass m and radius R is released from rest at a height h and rolls without slipping down a ramp. What is the velocity of the center of the disk when it reaches the bottom of the slope? (Hint Use the work-energy principle. At each instant the disk rotates around the contact point C, thus the inertia used for rotatonal kinetic energy should be computed around point C not point G.) m G

A disk with mass m and radius R is released from rest at a height h and rolls without slipping down a ramp. What is the velocity of the center of the disk when it reaches the bottom of the slope? (Hint Use the work-energy principle. At each instant the disk rotates around the contact point C, thus the inertia used for rotatonal kinetic energy should be computed around point C not point G.) m G

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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Clutches, Brakes, Couplings, and Flywheels

The clutch is described as a machine element used to connect or disconnect two shafts together to transmit torque or power. The clutch works on the principles of friction. The clutch is commonly used in automobiles to transfer power from the driving shaft to the driven shaft.

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**Problem Statement:**

A disk with mass \( m \) and radius \( R \) is released from rest at a height \( h \) and rolls without slipping down a ramp. What is the velocity of the center of the disk when it reaches the bottom of the slope?

*(Hint: Use the work-energy principle. At each instant the disk rotates around the contact point \( C \), thus the inertia used for rotational kinetic energy should be computed around point \( C \) not point \( G \).)*

**Diagram Explanation:**

The diagram shows a ramp inclined to the horizontal. A disk is positioned at the top of the ramp. The disk has a center of mass at point \( G \) and a contact point with the ramp at \( C \). The radius of the disk is indicated as \( R \), and the height from which the disk is released is shown as \( h \). The forces acting on the disk due to gravity will cause it to roll down the ramp.

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