How Does Friction Affect the Acceleration of a Spool in Rotational Motion?

AI Thread Summary
Friction plays a crucial role in determining the acceleration of a spool in rotational motion. The problem involves a spool unwinding under a constant force, where the acceleration of the center of mass is calculated to be 4F/3M. Additionally, the force of friction acts in the same direction as the applied force F and is determined to be F/3. To solve for the frictional force, applying Newton's 2nd Law is essential, as it relates the net force to the acceleration. Understanding these relationships is key to solving problems involving rotational motion and friction.
smt
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I'm studying the chapter on rotational motion, and I have a problem that I don't have a clue how to solve, the problem is this: A spool of wire of mass M and radius R is unwound under a constant force F. (F is parallel to the ground) Assuming the spool is a uniform solid cylinder that doesn't slip, show that (a) the acceleration of the center of mass is 4F/3M, and (b) the force of friction is to the right, (same direction as F) and equal in magnitude to F/3.

(b) is the part I really don't have a clue on, can anyone help me solve this problem?

thanks in advance,

smt
 
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Well you should show work but it's very simple-- use Newton's 2nd Law to solve (b). You know the acceleration and thus the net force which must be the sum of F and f.
 
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