Linear Momentum of Unwinding Cylinder

[jamaicanking]

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?

 

[kuruman]

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).