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I'm not sure that I understand this problem:

A spool of wire of mass 4.7kg and radius 0.99m is unwound under a constant wire tension 10N. Assume the spool is a uniform solid cylinder that rolls without slipping. Find the friction force on the bottom of the spool.

Image

(Note that the wire is coming out of the top of the spool)

The frictional force is equal to the coefficient of friction * the normal force.

I can easily find the normal force by multiplying the mass times 9.8 m/s^2, but nowhere does the problem state the coefficient of friction.

Aside from that, a rolling object isn't affected by the frictional force. I tried 0 and that's not the answer, so there is a frictional force here.

What am I missing here? There doesn't seem to be nearly enough information to calculate the frictional force.

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In Mechanics, whenever you see the expression "rolling without slipping" it means that there is only static friction (without kinetic friction). This means that the only contact between two objects is momentarily stationary so that the contact force is of static friction essence applied tangentionally along the contact surface. I hope this will give you a hint of how to approach the problem. If you can make a picture of your setup, it would be a great help for yourselves as well as future readers. Sincerely,

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The frictional force is equal to the coefficient of friction * the normal force.

This is true for kinetic (sliding) friction, but is not true for static friction. In the non-sliding case, the coefficient of friction times the normal force instead give a maximum value for the frictional force, not necessarily the actual amount.

Since the force may be less than this amount, you don't need the actual coefficient of friction, and you can't use this formula to find the force.

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If you look at your picture and if $F$ was the only force which was acting then the linear acceleration $a$ of the centre of mass would be given by $F = Ma$ and the angular acceleration about the centre of mass would be given by $FR = I_{cm} \alpha = \frac 12 MR^2 \alpha$.

The no slipping condition $a = R \alpha$ is not satisfied so there must be another force present - the static frictional force between the object and the ground.

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