Cylinder rolling on fixed cylinder

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The discussion centers on the dynamics of a cylinder rolling on a fixed cylinder, specifically addressing the equations of motion involved. A differential equation was proposed: \(\ddot{\theta} + \frac{2g}{3(a+b)} \sin(\theta) = 0\). However, the variables 'a' and 'b' were not defined in the problem statement, leading to confusion. Participants emphasized the importance of accurately determining kinematics to solve the problem effectively.

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Check Attached file for questionI am not able to get the equations for motion. Except that when cylinder loses contact, the normal force is zero.Please answer this fast. Need it for a test tomorrow. Thanks a lot!
 

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Ok, I tried the question for some time and came up with this differential equation,

\ddot{\theta} + \frac{2g}{3(a+b)} \sin(\theta) = 0
 
What are a and b; they do not appear in the problem statement.

Did you get the kinematics correct? This is where most people get off track on a problem of this sort, so look very closely at that aspect.
 

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