Rolling without slipping, theory

[HaoPhysics]

Homework Statement

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.

Homework Equations

And

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?

 

[BvU]

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

 

[HaoPhysics]

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

Oops! Yeah I changed it.

 

[BvU]

But the resource I'm looking at

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

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

 

[HaoPhysics]

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

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

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)

 

[haruspex]

Is this correct then?

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

 

[HaoPhysics]

Retry that last step.

 

[haruspex]

View attachment 199501

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

 

[HaoPhysics]

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

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:

 

[haruspex]

View attachment 199503

No, a_cm is not F/M.

I am not sure how to get R in there.

As I wrote, a subset of those variables is fine. It just must not involve any variables outside of the given set.

 

[HaoPhysics]

No, a_cm 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.

Oops! a_cm is net force / m,

 

[haruspex]

Oops! a_cm is net force / m,

View attachment 199748

Looks right.