   Chapter 8, Problem 69P

Chapter
Section
Textbook Problem

A solid, horizontal cylinder of mass 10.0 kg and radius 1.00 m rotates with an angular speed of 7.00 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system.

To determine
The final angular speed of the system.

Explanation

Given info: The mass of the cylinder is 10.0kg , radius of the cylinder is 1.00m , the initial angular speed of the cylinder is 7.00rad/s , mass of the putty is 0.250kg , and the distance of the putty from center of the cylinder is 0.900m .

Explanation: The moment of inertia of the cylinder before the putty dropped on it is Ii=(1/2)MR2 and the final moment of inertia of the cylinder after the putty sticks with it is If=Ii+mr2 . Now from conservation of angular momentum Ifωf=Iiωi and using this expression, the final angular speed of the system is calculated.

The formula for the final angular speed of the system is,

ωf=(MR2MR2+2mr2)ωi

• M is mass of the cylinder.
• R is radius of the cylinder.
• m is mass of the putty.
• r is the distance of the putty from center of the cylinder.
• ωi is initial angular speed of the cylinder

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