Unwinding Cylinder

1. The problem statement, all variables and given/known data
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.

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

3. 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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