Acceleration of the center of mass of this cylinder

AI Thread Summary
The discussion focuses on calculating the acceleration of a hollow cylinder's center of mass when subjected to a pulling force. The moment of inertia is correctly identified as 0.5m(r(out)^2 + r(in)^2), but there is confusion regarding the mass value used in calculations. Participants emphasize the importance of considering frictional torque, which complicates the equations for torque and acceleration. They suggest applying Newton's second law in the horizontal direction to solve for acceleration accurately. Properly accounting for all forces and torques is essential for determining the cylinder's acceleration.
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A 2.81 kg hollow cylinder with inner radius 0.29 m and outer radius 0.5 m rolls without slipping when it is pulled by a horizontal string with a force of 47.7 N, as shown in the diagram below.

Its moment of inertia about the center of mass is .5m(r(out)^2 + r(in)^2).

What is the accelereation of the cylinder's center of mass? Answer in units of m/s^2.


What am I doing wrong? I found the Torque of the hollow cylinder by T = F(r). Then I found the angular acceleration by Torque = Interia * Alpha. Inertia was found using the supplied forumula. After finding the angular acceleration I found the Tangential Acceleration by TangentialAcceleration = radius * AngularAcceleration. What am I doing wrong?
 
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Isn't the moment of inertia of a hollow cylinder
\frac{1}{2} M (R_1^2 + R_2^2)
So, your value of M/2 is not 0.5 but 2.81/2
 
siddharth said:
Isn't the moment of inertia of a hollow cylinder
\frac{1}{2} M (R_1^2 + R_2^2)
So, your value of M/2 is not 0.5 but 2.81/2

Hence, .5M which is the same as 2.81/2.
 
Oh, you mean 0.5 * 2.81 . Didn't see that, sorry.

There wil be a torque due to friction, the value of which is not known. So, I don't think you can use the above equations alone to get the answer.

Have you applied Newton's second law in the horizontal direction? (ie, F-f = ma). Then eliminate f using all the equations and solve for a. That should give you the correct answer.
 
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