# Homework Help: Rolling without slipping, theory

1. May 6, 2017

### HaoPhysics

1. The problem statement, all variables and given/known data
I am solving a question that asks for, what's the minimum coefficient of friction required for a cylinder to roll without slipping? Where the cylinder has a force F acting on its center.

2. Relevant equations

And

3. The attempt at a solution
From the way I understand it, the only torque acting on the cylinder is the torque from friction, since the torque from force F is acting at the center, thus resulting in 0 torque.

But the resource I'm looking at assumes that torque from friction is not the only torque acting on the cylinder. But it doesn't explain why.

Where are the other torques acting from?

Last edited: May 6, 2017
2. May 6, 2017

### BvU

Your problem statement may be incomplete. Zero is the answer as it is written now.

3. May 6, 2017

### HaoPhysics

Oops! Yeah I changed it.

4. May 6, 2017

### BvU

Tell us what you see. Our telepathic capabilities are limited.

And: what do you do with the given 'rolling without slipping' ?

5. May 6, 2017

### HaoPhysics

http://www.feynmanlectures.info/solutions/roll_without_slipping_sol_1.pdf
On step 6, it says, "In order for the ball not to slip, the torque on the ball from friction can not be less than the total torque on the ball when it rolls"
(Note: I tweaked the problem from a slope to a flat ground for simplification purposes, so I don't have to worry about the theta for now)

Well since it is rolling without slipping, the linear acceleration must equal to angular acceleration multiplied by radius:

So since the sum of torques is the torque from friction:

Is this correct then?

(Sorry about the really big pictures)

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6. May 6, 2017

### haruspex

Retry that last step.
Also, your answer should express μmin in terms of F, M, g and R (or any subset of those).

7. May 6, 2017

8. May 6, 2017

### haruspex

That's better. But see the edit I made to my previous post.

9. May 6, 2017

### HaoPhysics

Hm..

The only substitution which I can make is this:

I am not sure how to get R in there.
It seems that the coefficient of fric. is not dependent on R.

Interesting, this follows:

10. May 6, 2017

### haruspex

No, acm is not F/M.
As I wrote, a subset of those variables is fine. It just must not involve any variables outside of the given set.

11. May 7, 2017

### HaoPhysics

Oops! acm is net force / m,