a cylinder is  given an initial angular velocity w and is placed on an incline with angle of incl., @ . given that

coefficent of friction < tan@  ,  then describe the motion of the cylinder  on the plane .

waiting for the concept regarding above question..............................

in my earlier post coeff., of friction was = tan@.

but now i am asking if it is coeff., < tan@.

see weather i am right or not...............

firstly friction will act upward which will be trying to reduce the angular velocity but  at the same time the cylinder

will be in down ward  linear motion.

but when angular velocity becomes zero (  linear velocity not equal to zero ) what is the motion of the cylinder

from here ........................

this is where i am not able to understand.........

will it start rolling as soon as w becomes zero (  if friction is sufficient to prevent slipping)

or will it slide for sometime and then start pure rolling or what.....................

waitng for the reply.................................

if possible please give me the equations........................please..................

if possible please give me the equations........................please..................

if possible please give,me the approtpriate eqations................

any one please answer to my previous post.......................................................

any one please answer to my previous post.......................................................

hey i m also confused still i m trying

since there is not sufficient friction to support pure rolling so the cylinder will slip at the point of contact

as the ang vel given is clockwise so friction will be in upward dir but there will be mgsin@ in downward dir.

since  <tan@ so frictional force will be less so the cylinder will slip downwards.

tell me if i m right?

The figure isn't clear.

I am assuming the direction of angular velocity  to be clockwise

Then the bottommost point slips down the incline and hence friction is up the incline.

Now, as

And hence the acceleration of the CM is down the plane, which will lead to a translational velocity down the plane. And the angular velocity being clockwise, the velocity of point of contact is downward. The cylinder moves downward, and after the angular velocity reduces to zero due to the anticlockwise torque, a counterclockwise angular velocity is created due to friction, that after sometime will lead to pure rolling.

But essentially, the cylinder can't climb the inclined plane if  

since the cyl., is rotating in the anti- clockwise sense, friction is upward.

this will reduce the agular vel., of the cylinder.

but the cyl., will continue moving linearly downward since the downward force along the plane is greater

than the friction which is upward.

due to the angular retardation, at some point of time , the angular velocity which is in the anticlockwise sense

will bcom zero.

after this i dont know what will be the motion..................

i think 

as soon as the  angular vel., bcomes zero ,if friction is sufficient to prevent slipping , the cyl. will start rolling.

but if friction is not sufficient to prevent slipping ,  cyl., will slide.

but i am not confident about the above two lines...........................

i want anyone to anwer to my doubt ,,,,,,,,,,,,,,,,,,,,,,,,,,,,.............................waiting for the reply...............

elessar i have under stood what u have said........but listen to my doubt and clarify it to me please......

 --------  if friction is sufficent to prevent slipping ,then tell me weather the cyl. will start pure rolling as

soon as angular vel bcomes zero or wil it slide for some time and then starts pure rolling.?

---------what will be the value of friction as soon as angular vel., bcomes zero.  tell  me weather it will adjust

itself  so as to bring pure rolling to the cyl.,. ( assume friction is suff., to prevent slipping)