Rolling Resistance without slipping

[andyrk]

We know that in real world scenarios, for rolling without slipping of bodies like sphere, dis, cylinder etc. there is a rolling resistance present. This rolling resistance comes from the fact that in actual situations bodies aren't perfectly rigid. So there is some compression at the point of contact between the rolling body and the surface. According to what I have read, this compression is unevenly distributed even at the point of contact. Like it means if we maginfy and see the point of contact we would notice that some parts (very small elements) of the points of contact are more compressed and some are lesser. But why does this happen? And on account of this there is a net resultant force which doesn't pass through the CM of the rolling body and so this produces an anticlockwise torque which in turn slows down the object. So my second query is that even if the compression's are uneven how does it effect the net normal reaction force? I thoroughly read the following link but couldn't get anything more out of than what I have written: http://www.lhup.edu/~dsimanek/scenario/rolling.htm

 

[Simon Bridge]

...if we maginfy and see the point of contact we would notice that some parts (very small elements) of the points of contact are more compressed and some are lesser. But why does this happen?

How does what happen - you already pointed out that the body is not totally rigid?

Mode the rolling object as a lot of small masses connected by stiff springs - it's own weight will compress the springs close to the floor more than those at the top. If it is not rolling, then the normal forces along the deformed region are symmetric.

The answer to both your queries follows.

 

[andyrk]

Can you please explain it a bit more? I got confused.. My queries are:
(1)Why are compression's uneven at the point of contact?
(2)Even if the compression's are uneven how do they effect the net normal reaction force? That is why is the net normal reaction a bit to the side of the Centre of Mass? I know this is because the Normal Reaction Forces are greater on the side where there are more compressions but why is that?

Thanks.

 

[Simon Bridge]

Can you please explain it a bit more? I got confused..

You get reaction forces because the object only presses down so far into the surface. Your link has a good picture of a round object deformed as it presses into the surface.

If the object were not rolling - the compressions over the area of contact will be symmetrical. Therefore the reaction forces will be symmetrical. They still won't be uniform - the compressions directly below the center of mass will be higher. So the reaction force there will be higher. Can you see why this is the case?

If the object is rolling, then there is a torque pressing down at the front and pulling up at the back - so the reaction forces are higher at the front than at the back.

To see it happen, fill a balloon with water and get it to roll - watch carefully as the surface deforms.

 

[voko]

As stated in the linked article, rolling resistance is primarily hysteretic. Deforming something takes more energy than is recovered from relaxation.

 

[CWatters]

Can you please explain it a bit more? I got confused.. My queries are:
(1)Why are compression's uneven at the point of contact?
(2)Even if the compression's are uneven how do they effect the net normal reaction force? That is why is the net normal reaction a bit to the side of the Centre of Mass? I know this is because the Normal Reaction Forces are greater on the side where there are more compressions but why is that?

Thanks.

It's because the ball is moving.

Compare the situation with a boat moving through water. There is always going to be more force on the front of the boat.