Rolling Friction

‘My explanation’ to – rolling friction – its direction – possible reasons

Consider a rolling body, no external force other than gravity and some force from ground – which is proportional to the mass of the body (alone?) acting on it.

In due course of time, the velocity of the c.m of the body decreases, also the angular velocity – which implies that an external force against the direction of motion acts on the body, and also a torque.

Now as we know the instantaneous centre of rotation of a rolling body is the point of contact with the ground.

Also at every instant the rolling body is acted upon by a torque due to force from the ground. And the force(s) from the ground can be added to a single point force.

Now if we consider rolling as a single point contact motion – the force should act at that point… But if that is assumed, then the force can’t create a torque about the axis of rotation.

Doesn’t that mean, the force acting has an offset about the point of rolling???
Also the force can come through a contact only – Doesn’t that imply that there are multiple points of contact – and only if we assume multiple points of contact, we can explain the rolling friction???

So rolling with rolling friction implies multiple contact points…

NOW DIRECTION / LINE OF ACTION OF THE FORCE FROM THE GROUND.

The vertical component of force from the ground definitely will be of magnitude equal to the weight of the body. So the horizontal is the rolling friction force.

Definitely, the rolling friction force from the ground cannot act through the point about which rolling is taking place.

We assume the lowest point of the rolling body is the point of rotation – I will try to explain the validity of this assumption later.

See the figure below.

The blue arrow cannot be the line of action – it wont create a torque
The green arrow – will create a torque aiding the rotation – increase angular velocity.
The red arrow – the possible solution – or ‘MY solution’

Now Analyzing the solution.


The rolling friction force will create a torque opposing the rotation – also oppose the linear motion. And the factor that create the torque against the rolling is reaction to gravity??? or some relation to it??? – (this is perplexing to me also)
The vertical reaction from the ground will have an off set, if the vertical forces are equaly distributed through the points of contact - which need not be true.
But again a slight offset can be expected.

Also the validity of assumption I mentioned – if it is not there gravity or reaction to gravity will do the magic.

Does that mean – if the same setup taken to moon will roll for longer time?? – It can’t be, because the linear deceleration being experienced by body is same(or?).

Explaining the solution.

Before that let us try to analyze what is the origin of the horizontal force…

Some people say – I also believe – this horizontal force is due to the deformation of the ground under the weight of the body. And because of this, the point contact changes to line contact – on one side attraction and other side repulsion.

The repulsion will be greater – I believe because it is trying to ‘squeeze into the territory of the ground’.

Now if we go by that – the deformation of surface in outer space will be virtually zero(gravity between two will make surface deform) – no deformation – virtually no forces – as it balances – no rolling friction – rolls for ever??

And moon – it should roll more…

Now I feel like I have completed a science fiction. Don’t know what all foolishness, but nice to think…