Friction force in rotational motion

[daivinhtran]

My textbook says, "for an object rolling without slipping down an incline, the frictional force fs is less than or equal to its maximum value. fs < μsFn

Why is that? What happen it's greater than??

When do we have static friction in rotational motion? (for rolling object)

Then in an example problem about rolling with slipping, it says "there is slipping so the friction is kinetic (not static).? Same question. ==> Why?

 

[rahulpark]

For the first question,
friction as in all conditions has a limit.(well u know it). If it weren't that way the world wouldn't function into dynamics(only rotation). down a plane, friction has limit μ*mg*cosθ.if it weren't the way it were, there wouldn't be any slipping. For the moment it might look like it's good. But think like everything stuck to everything.

For second Q,
As you can see that the point of contact in rolling without slipping is at rest.friction acts against the relative motion b/w contact points. That's the work of friction (static).
If you wan't to cause a change in the velocity profile, you have to go against static friction.
For visualization , think a rotating object with spurs (gears) on a profiled (as in the gear) plane.
If it were rolling without slipping, the gear tooth will exactly match into the profiled plane. So there isn't any relative motion b/w the object's point of contact and the plane. If you like to alter the motion you would have to move uphill (That is the static friction in microscopic scale)
causing a relative speed at that instant. If it gains velocity (with slipping) it has inertia . So it turns to dynamic friction. So ,all matters is the relative speed b/w point of contact and the ground (not the body's velocity with the ground)

 

[daivinhtran]

For the first question,
friction as in all conditions has a limit.(well u know it). If it weren't that way the world wouldn't function into dynamics(only rotation). down a plane, friction has limit μ*mg*cosθ.if it weren't the way it were, there wouldn't be any slipping. For the moment it might look like it's good. But think like everything stuck to everything.

For second Q,
As you can see that the point of contact in rolling without slipping is at rest.friction acts against the relative motion b/w contact points. That's the work of friction (static).
If you wan't to cause a change in the velocity profile, you have to go against static friction.
For visualization , think a rotating object with spurs (gears) on a profiled (as in the gear) plane.
If it were rolling without slipping, the gear tooth will exactly match into the profiled plane. So there isn't any relative motion b/w the object's point of contact and the plane. If you like to alter the motion you would have to move uphill (That is the static friction in microscopic scale)
causing a relative speed at that instant. If it gains velocity (with slipping) it has inertia . So it turns to dynamic friction. So ,all matters is the relative speed b/w point of contact and the ground (not the body's velocity with the ground)

So what happen if fs > μsFn?

 

[ehild]

So what happen if fs > μsFn?

It can not happen. The static friction can not be grater than μsFn.

When you pull an object, resting on the ground, with force F, and F<μsFn the object stays in rest. If the object can roll, it will roll.

If you pull an object with force F>μsFn it will slip.

ehild

 

[rahulpark]

So what happen if fs > μsFn?

what does fs in ur statement mean? frictional force or applied force