What Is the Maximum Inclination for a Cylinder to Roll Without Slipping?

[Punchlinegirl]

A block of a certain material begins to slide on an inclined plane when the plane is inclined to an angle of 14.57°. If a solid cyclinder is fashioned from the same material, what will be the maximum angle at which it will roll without slipping on the plane?

I really have no idea where to start on this problem since the only given is the angle. I know that the moment of inertia of a cylinder is (1/2)MR^2 if that's needed at all. Any hints?

 

[Päällikkö]

In what case does the cylinder slip (hint: friction)?
Another hint: total acceleration is the same as the tangential acceleration if there's no slipping.

(Would you happen to have the correct answer?)

 

[Kenny Lee]

I'm having trouble with a similar problem.

I tried finding the coeff of friction; got an arctan14.7 ...

Then I set up the dynamics equations of the cylinder, taking the center of mass as the center of rotation; Wx - friction = ma

And then I put in no slipping condition i.e a = (angular acceleration) X R.

I substitude (angular acceleration) with the relevant expression using Newton's second law in angular form.

I solve and then I get a very unlikely value of 89 degrees. Where am I wrong.

 

[Päällikkö]

I'm having trouble with a similar problem.
I tried finding the coeff of friction; got an arctan14.7 ...

According to my calculations you should get a plain tan (not arctan).

Then I set up the dynamics equations of the cylinder, taking the center of mass as the center of rotation; Wx - friction = ma
And then I put in no slipping condition i.e a = (angular acceleration) X R.
I substitude (angular acceleration) with the relevant expression using Newton's second law in angular form.
I solve and then I get a very unlikely value of 89 degrees. Where am I wrong.

The rest sounds, if I understood everything correctly, fine.

 

[Kenny Lee]

Oh right. Yea, tan 14.7 degrees. Thanks.
okay now i get 38 degrees... dat bout right?

 

[Punchlinegirl]

I see how to do it now. Thank you

 

[Päällikkö]

Oh right. Yea, tan 14.7 degrees. Thanks.
okay now i get 38 degrees... dat bout right?

If you mean the problem in this thread (with the angle actually being 14.57), I get the same answer.

I see how to do it now. Thank you

No problem .

 

[m_sepehr82]

romured question

A block of a certain material begins to slide on an inclined plane when the plane is inclined to an angle of 14.57°. If a solid cyclinder is fashioned from the same material, what will be the maximum angle at which it will roll without slipping on the plane?
I really have no idea where to start on this problem since the only given is the angle. I know that the moment of inertia of a cylinder is (1/2)MR^2 if that's needed at all. Any hints?

i think that it's a romured question in which the answer is 14.57 degree because friction doesn't pertain to shape of the block or how much is the surface of that
i think the answer is that