In a continuous printing process, paper roll is wrapped on a cylindrical core which is free to rotate about a fixed horizontal axis. The paper is drawn into the process at a constant speed v, as shown in the figure. If r is the radius of paper on the roll at any given time and b is the thickness of the paper, then the angular acceleration of the roll at this instant is
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In a continuous printing process suppose the total length of paper is 
.
If r 1 is the inner radius of roll then, 
...(i)
And at this moment, 
...(ii)
Differentiating equation (i) w.r.t. time,
Differentiating equation (ii) w.r.t time
…(iv)
Using (iii) and (iv), 
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