Pure Rolling: Is Speed of Point of Contact Really 0?

[pardesi]

when we say that in pure rolling the speed of the point of contact is 0 do we really mean it's just absolutely 0 or is it negligible.this may seem strange...
but if it's 0 then why does that point ever move.if it ever moves then it's speed is no more 0 ...

 

[rcgldr]

It's the speed of the point relative to the surface at the point of contact. In real life, there's deformation, and there's a contact patch area, and in part of this area, there's no relative movement between the surfaces.

 

[pardesi]

yes that's ok if the speed is 0 why does the point move at all...if it moves then how can the speed be 0

 

[russ_watters]

The speed is zero for zero seconds - an instant, a single point in time. It is accelerating (actually decelerating, then accelerating).

 

[pardesi]

well 'speed' of every point is 0 for 0 sec.well i even thought about that accelataion concept but anyway till the bod is in contact with the surface it's speed must be 0 even if it has accelaration it has to move then the speed becoems non 0

 

[cesiumfrog]

Forget rolling wheels for a second, the circle is a bit complex (tyre comes down, touches "statically" then goes up..).

Think about the tread of an army tank instead. Think about the bit under the middle of the tank. It's flat like the surface of the ground, and moves at the same speed as the ground (viz. 0). The tank engine basically pushes this section of the tread backwards (although it doesn't move, being supported well by friction) and hence (by Newton's 3rd law) the tread pushes forward the tank (accelerating th' engine and all that isn't in frictional contact with the ground). Meanwhile, since the tank has moved forward, it has to pick up the back pieces of tread, and put them down at the front (otherwise I would have merely described a rocket engine, or a water balloon without the knot at the neck).

 

[Cyrus]

I like that tank analogy.

 

[pardesi]

yes that's ok but my doubt is consider the point on the 'tip' of a circle when we say it's speed is 0 do we really meant that.because the point of contact keeps on changing.what i mean to say that is the point actually at rest or that mathematically
$$\lim _{\Delta t \to\ 0} \frac{\Delta \vec {r}}{\Delta t}=0$$

i seriously believe it is the second mathematical interpretation.
but thsi would simply imply friction is a mathematical genius

 

[cesiumfrog]

i mean to [ask] is the point actually at rest or [just mathematically]

Philosophy now? If I'm driving at 60, then break to a halt for a red light, was my speed ever 30km/hr?

I'm curious what your opinion is. Mathematically, you can prove the answer to be yes. Actually, well, actually it is whatever the maths says it is. *shrug*

 

[pardesi]

right mathematically yes but in physics sense who cares i will never measure or see or even feel that.

 

[cesiumfrog]

Go imagine pointing a radar speed gun at a pendulum to measure if it "really" stops at the top of each swing.

 

[pardesi]

i really don't get it consider the point just attached to the Earth ...we say it's speed is 0 ..yes it does move but when it does it's speed is non 0 and it slips ...so how is this explanied

 

[uiulic]

Can I ask further

1 What's the difference among rolling,rotation,sliding and slip, which are the frequent words used for a particle (say just a sphere)?
2 I remember I heard about rolling friction and sliding friction in engineering mechanics course. What 's their difference? Their friction coefficients are often assumed to be the same?
3 For a two sphere system, two spheres are moving to each other (any kind of move u can imagine)? How to calculate the displacements caused by rolling, rotation,sliding respectively?

Thanks
best regards

 

[AlephZero]

i really don't get it consider the point just attached to the Earth ...we say it's speed is 0 ..yes it does move but when it does it's speed is non 0 and it slips ...so how is this explanied

It moves, but it doesn't slip.

For circular motion the accleration is towards the centre. The point leaves the ground moving vertically upwards, moves in a curve, and finally moves vertically down, and touches the ground as it reverses direction, and moves vertically up again.

The curve the point follows between two points of contact with the ground is called a cycloid. Google "cycloid" and check out the geometry.

 

[pardesi]

so basically if i got u right the friction prevents relative slipping between two points in the direction along the tagent to both of them and it does so here and since there is a net upward unbalanced force the pointmoves vertically upward instantaneously hence friction does achieve it's aim