Investigation of a Rotating Cylinder

[Zalajbeg]

Hello all,

I have some confusion about rotating. The bad thing is that I don't know where the point is which my confusion starts. As I want to check also my fundamental knowledge about the topic I will ask my questions step by step to see where my problem begins. I hope you don't mind.

My first questions are those:

Let us roll a rigid cylinder on a rigid surface (whose height is always h=0), we only give the first velocity, after that there is no force on the system externally applied.

- I think the only forces exert on the cylinder are the weight of the cylinder, the vertical reaction force exerted by the ground and the horizontal friction force which is in the same direction with the movement of the center of mass. Is it right?

- If so, the total horizontal force is the frictional force. As it is in the same direction with the movement of the center of mass will the cylinder accelerate forever?

 

[A.T.]

the horizontal friction force which is in the same direction with the movement of the center of mass.

In ideal level rolling there is no horizontal friction. In real level roiling without sliding there is rolling resistance due to deformation and horizontal friction, but definitely not in the direction of motion, but opposite to it.

will the cylinder accelerate forever?

Shouldn't that conclusion give you a hint that you got the direction of the force wrong?

 

[valerioperi]

Are you sure that the frictional force has the same direction as the the movement of the center of mass? Will it round clockwise or anti-clockwise if it's like that?

@A.T maybe I'm wrong, but there is a static (not one which dissipates energy) frictional force or otherwise (unless you gave some angular momentun at the beginning) it wouldn't rotate at all, isn't it?

 

[A.T.]

@A.T maybe I'm wrong, but there is a static (not one which dissipates energy) frictional force or otherwise (unless you gave some angular momentun at the beginning) it wouldn't rotate at all, isn't it?

I'm talking about what happens after you released it rolling, not how it got in that state.

 

[Zalajbeg]

All,

Thanks for your replies. @valerioperi: One of the problems I am confused is what you say.

I will reason my idea:

- The contact point doesn't move.
- The static friction force exerts against to the direction of the movement tendency.
- If the cylinder is moving to right the point of contact will have a tendency to move left.
- Then the static friction must exert on the point of contact and the direction must be right. I think this is the reason why the contact point doesn't move.

Could you please explain me which are these statements are wrong?

 

[valerioperi]

Is it rolling without sliding?

@A.T. Ok, I agree

 

[Zalajbeg]

Yes, it is rolling without sliding.

 

[valerioperi]

In the ideal world if there is no friction and the body was already rolling it will go on rolling with the same linear and angular velocity. On the other hand if there's friction try to figure out which direction it should have to make it roll clockwise. If the contact point is static and no force is acting on him except the frictional force how you determine which is the direction of its tendency of motion?

 

[Zalajbeg]

Thanks for your replies. I think I have understood your logic. I wished I could find this link before:

http://www.phy.davidson.edu/fachome/dmb/PY430/Friction/rolling.html

It explains the situation.

If we talk about the start of the motion is the free body diagram in the link correct? If so, it will be confusing again.

 

[A.T.]

Could you please explain me which are these statements are wrong?

The point of contact doesn't accelerate horizontally because the static friction to the left on the contact point is balanced by internal forces to the right from the wheel which is slowing down.

 

[valerioperi]

The first or the second diagaram? The first doesn't deal with an ideal pure rolling motion so the situation is quite different and a bit more complicated.

 

[Zalajbeg]

The point of contact doesn't accelerate horizontally because the static friction to the left on the contact point is balanced by internal forces to the right from the wheel which is slowing down.

I am sorry but it confuses me again. For pure rolling is there a static friction or not?

The first or the second diagaram? The first doesn't deal with an ideal pure rolling motion so the situation is quite different and a bit more complicated.

I am talking about the first diagram. It seems logical to me as the torque forces (not the physical term) the contact point to slide to left. However this time I am thinking about this problem:


- I assume the first diagram in the link is correct.
- Let us say I am trying to start the motion by pushing the top point of the cylinder.
- Then if I don't exert a force greater than the maximum static friction force I will have a free body diagram which shows two equal(?) forces: Static friction to the right and the force exerted on top of the cylinder to right. Then how can it rotate? Won't it slide to right?

 

[A.T.]

For pure rolling is there a static friction or not?

In ideal rolling without rolling resistance, no. But when the wheel deforms and slows down, it needs an external horizontal force opposite to motion, which is the static friction. If the road deforms too, the horizontal braking force might also be provided by local normal force, on the incline.

 

[Zalajbeg]

In ideal rolling without rolling resistance, no. But when the wheel deforms and slows down, it needs an external horizontal force opposite to motion, which is the static friction.

Thanks for the explanation.

Now, I have understood if there is no deformation and slipping there is no horizontal friction force in pure rolling.

I will be very pleased if I can learn a bit about the start of the motion. (The condition with acceleration.)

I have shared a link above. It shows the frictional force in the same direction as the motion. I understand from that if a torque is applied the cylinder will be forced to slip to left. Therefore thw horizontal friction force is towards right.

In examples about rolling on an inclined plane the horizontal friction force is in the opposite direction of the motion. I understand that the horizontal component of the force of gravity will try to slip the contact point to the motion direction. However it will also create a torque on the contact point which will try to slip the contact point to the opposite direction. Will the horizontal friction force be the difference between these effects?

 

[A.T.]

I have shared a link above. It shows the frictional force in the same direction as the motion. I understand from that if a torque is applied the cylinder will be forced to slip to left. Therefore thw horizontal friction force is towards right.

In examples about rolling on an inclined plane the horizontal friction force is in the opposite direction of the motion. I understand that the horizontal component of the force of gravity will try to slip the contact point to the motion direction. However it will also create a torque on the contact point which will try to slip the contact point to the opposite direction. Will the horizontal friction force be the difference between these effects?

The direction of friction during acceleration depends on how much net linear force vs. torque you apply to propel the wheel. Depending on the mass vs. moment of inertia there are combinations of applied linear force and torque that result in zero static friction during acceleration. Deviating from that ratio one way or the other will result in static friction pointing one way or the other.

 

[Zalajbeg]

The direction of friction during acceleration depends on how much net linear force vs. torque you apply to propel the wheel. Depending on the mass vs. moment of inertia there are combinations of applied linear force and torque that result in zero static friction during acceleration. Deviating from that ratio one way or the other will result in static friction pointing one way or the other.

Thank you very much for your help. I was wondering if the direction is determined directly. I understand from my search on the web that there are specific situations which direction can be determined easily.

I understand the logic now. Thank you very much again.