Linear Momentum of Unwinding Cylinder

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To find the linear momentum of an unwinding cylinder, the relevant equations include momentum (P = mv) and the moment of inertia (I = 1/2 MR^2). The distance from the ceiling to the unwound point on the cylinder is represented as y = l, where l is the length of the string unwound. The momentum can be expressed as m*dl(t)/dt, indicating the rate of change of the unwound length. By drawing a free body diagram and applying Newton's Second Law for both rotational and linear motion, one can derive the linear acceleration and subsequently determine l(t). Understanding these principles is crucial for solving the problem effectively.
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Homework Statement


Find the Linear momentum of an unwinding Cylinder with one end of a string attached to the ceiling. The mass of the cylinder is m and radius r. The cylinder is uniform and there is no slipping.


Homework Equations


Momentum, P = mv
moment of inertia , I = 1/2 MR^2


The Attempt at a Solution


distance from ceiling to point on cylinder , y = l(length of string unwound)

so is the momentum simply m*dl(t)/dt?
 
Last edited:
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Yes. Draw a free body diagram, apply Newton's Second Law for rotational and linear motion, find the linear acceleration and use it to find l(t).
 

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