A cylinder rolls without slipping

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    Cylinder Slipping
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Homework Help Overview

The discussion revolves around a physics problem involving a cylinder rolling without slipping. Participants are examining the effects of friction on the motion of the cylinder, particularly in relation to the forces acting on it and the coefficients of friction involved.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the assumptions regarding the type of friction acting on the cylinder, whether it should be treated as kinetic or static. There are discussions about the correct application of trigonometric functions to resolve forces and the implications of friction direction on motion.

Discussion Status

Some participants have provided guidance on ensuring correct trigonometric applications and understanding the nature of friction in this context. There is an ongoing exploration of the implications of friction direction and its effects on both translational and rotational motion.

Contextual Notes

Participants are navigating the complexities of the problem, including the transition from kinetic to static friction and the need for accurate force component analysis along the slope. There is an acknowledgment of potential misunderstandings regarding the nature of friction in rolling motion.

athrun200
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Homework Statement


See the attachment Q5

Homework Equations


The Attempt at a Solution


Let's begin with part (a) first.
After finishing this homework (see the second attachment), I suddenly noticed 1 thing. The friction will gradually decrease to zero and then change the direction to become same as the motion direction.
Therefore, my work on part (a) would be wrong. Since I assume the friction is a constant (mgμsinθ).
How do I fix it?

And also, is my way to find the minimum coeff of kinetic friction correct?

And for part (b), it is really that easy?
 

Attachments

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  • 2010Q5.jpg
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For part (a), make sure you use the correct trig functions when finding the components of the weight. Otherwise, looks good!

For part (b), the friction is no longer kinetic friction when rolling without slipping.
 
TSny said:
For part (a), make sure you use the correct trig functions when finding the components of the weight. Otherwise, looks good!

For part (b), the friction is no longer kinetic friction when rolling without slipping.
Is it possible to find out the static friction coefficient in this question? Or we can just let a new μ be static friction coefficient?

For part (a), do you mean that the friction would be either kinetic or static, there is not intermediate between them (i.e. the friction would increase or decrease from one to another)?
 
Last edited:
Part (a) looks good except for finding the correct expressions for the components of mg along the slope and perpendicular to the slope.

For part (b), you do not need a coefficient of friction. Just consider the torque and force equations and link them using the relation between linear and angular acceleration for rolling without slipping.
 
Thank you! I will change the sin and cos!
 
Oh, I found that the direction of the friction turns out to be to the left. Does it make sense?
 

Attachments

  • Q5correct.jpg
    Q5correct.jpg
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athrun200 said:
Oh, I found that the direction of the friction turns out to be to the left. Does it make sense?

Before rolling, the cylinder shifts downward so the kinetic friction acts in the opposite direction, upward along the slope. With that direction, friction accelerates rotation and decelerates translation.

ehild
 
athrun200 said:
Oh, I found that the direction of the friction turns out to be to the left. Does it make sense?

Yes. There has to be a clockwise torque about the CM in order to give a clockwise angular acceleration as the cylinder accelerates down the slope.
 

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