A cylinder of radius R is spinned and then placed  on an incline having coefficient of friction u = tan@ ( @is the

angle of incline). The cylinder contiues to spin without faling for time

a) rw / 3gsin@

b) rw / 2gsin@

c) rw / gsin@

d) 2rw / gsin@

in which direction does it move .

For this problem, try to understand what is happening. Here the sphere will roll back only if the reverse spin given to it becomes zero. It will become zero only if there is a torque which brings about the angular retardation.

Let us consider the axis of rotation at the point of contact:

Torque equation is : .

Using basic kinematics equation, we have : 0 =

Which gives .

ya the answer is rw/2gsin

another soln. is dat umgcos@=mgsin@.

so by eqn. of motion find wen vel. of pt. of contact is zero and den it will turn and go up due 2 friction.

rate dis

initial statement was derived by u=tan@

rate dis full

ans is (B)

am i correct --------

firstly the friction acts upward along the plane.

there is no linear motion during its reverse spin     since,         friction (upward along the plane)  =

mgsin@ = downward force along the plane = mgsin@ ). -------------------------( 1 )

when  angular velocity becomes zero, the friction which is acting upward along the plane reduces in magnitude

so that the cylinder starts coming downward. i.e, if  friction is still  mgsin@ ( maximum friction ) then from ( 1 ) it 

can not  move downward ( since the forces are equal in magnitude and opposite in direction).

this is what i have undersood.        please i want to confirm weather i am correct  or not...........

hello any one please answer to my above post................

im waiting for the reply.................

any one please...............i am waiting for the reply............

(b)

Assuming the initial spin to be clockwise.

The inital slip of the cylinder is down the plane. So friction acts up at its full magnitude

Now, as

Hence the cylinder had no acceleration. So the CM doesn't develop any velocity and so the cylinder doesn't move.

So,

The spinning stops at

After this the cylinder moves down