Rolling without slipping, theory

In summary, the conversation is about finding the minimum coefficient of friction required for a cylinder to roll without slipping when a force F is applied at its center. The solution involves considering the torque from friction and the total torque on the cylinder, as well as the relationship between linear and angular acceleration. The final answer can be expressed in terms of the given variables: F, M, g, and R.
  • #1
HaoPhysics
26
0

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.
upload_2017-5-6_19-1-53.png

Homework Equations


upload_2017-5-6_18-58-1.png

And
upload_2017-5-6_18-58-31.png


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:
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  • #2
Your problem statement may be incomplete. Zero is the answer as it is written now.
 
  • #3
BvU said:
Your problem statement may be incomplete. Zero is the answer as it is written now.
Oops! Yeah I changed it.
 
  • #4
HaoPhysics said:
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' ?
 
  • #5
BvU said:
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:
upload_2017-5-6_19-37-21.png


So since the sum of torques is the torque from friction:
upload_2017-5-6_19-43-13.png


Is this correct then?

(Sorry about the really big pictures)
 

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  • #6
HaoPhysics said:
Is this correct then?
Retry that last step.
Also, your answer should express μmin in terms of F, M, g and R (or any subset of those).
 
  • #7
haruspex said:
Retry that last step.

upload_2017-5-6_19-49-45.png


:doh:
 
  • #9
haruspex said:
That's better. But see the edit I made to my previous post.
Hm..

The only substitution which I can make is this:
upload_2017-5-6_20-11-35.png


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:

upload_2017-5-6_20-17-9.png
 
  • #10
HaoPhysics said:
No, acm is not F/M.
HaoPhysics said:
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.
 
  • #11
haruspex said:
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.
Oops! acm is net force / m,

upload_2017-5-7_11-30-26.png
 

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  • #12

1. What is rolling without slipping?

Rolling without slipping is a physical phenomenon in which a body, such as a wheel or ball, moves forward while simultaneously rotating without any sliding between the body and the surface it is rolling on.

2. How is rolling without slipping different from rolling with slipping?

Rolling with slipping occurs when there is friction between the body and the surface, causing the body to slide as it rotates. Rolling without slipping, on the other hand, occurs when there is no sliding between the body and the surface, meaning there is no friction present.

3. What are the conditions for rolling without slipping to occur?

In order for rolling without slipping to occur, there must be a balance between the forces of friction and the forces of rotation. This means that the torque applied to the body must be equal to the product of the body's radius and its linear acceleration.

4. What are some real-life examples of rolling without slipping?

Some common examples of rolling without slipping include a bicycle wheel rolling on the ground, a ball rolling down an incline plane, and a car's tires rolling on the road while it is in motion.

5. What is the significance of rolling without slipping in physics?

Rolling without slipping is important in physics because it demonstrates the relationship between rotational and translational motion. It also allows for more efficient and controlled movement, making it essential in the design of many machines and vehicles.

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