Minimum friction to roll an imperfect sphere on an incline

[Vriska]

Homework Statement

I have a sphere, it's imperfectly spherical, I put it on an incline and apparently it needs a minimum friction to start rolling or moving.

Homework Equations

I = 2/5 MR^2

torque = I*alpha = R x F

The Attempt at a Solution

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before anything, I don't get why there's a minimum friction even happening, there a torque and there's nothing to counter that, why wouldn't it roll huh?

So sphere's there, exerting a normal force of mgcos (o) where o is the angle of incline.

the friction results in torque around centre of mass

u(coeff of friction) * mg cos (o) * R = I * Alpha

u mg cos(o) = 2/5 ma - (i)

soo we need we need mg sin (o) - u mgcos(o) =ma = 5/2 u mg cos(o)

u = 2/7 tan(o) or something

but I don't get it,I don't get what I've done. if it had a greater or lesser coefficient of friction would it what - roll slower, roll faster? (i) seems to be suggesting that. That doesn't seem to make sense to me :/

 

[lekh2003]

why wouldn't it roll

It wouldn't roll, it would slide.

but I don't get it,I don't get what I've done. if it had a greater or lesser coefficient of friction would it what - roll slower, roll faster? (i) seems to be suggesting that. That doesn't seem to make sense to me :/

This is because you do not understand the entire concept of friction. Study static and kinetic friction and the difference. I would try and answer your queries, but it would only confuse you more.

 

[CWatters]

Homework Statement

I have a sphere, it's imperfectly spherical, I put it on an incline and apparently it needs a minimum friction to start rolling or moving.

That's wrong. No friction is needed to make it start moving (sliding). Friction is needed to start it rolling.

A cube is an imperfect sphere. Draw a diagram showing the forces acting on a cube and the conditions that need to make it tip over (aka roll).

 

[Vriska]

It wouldn't roll, it would slide.

This is because you do not understand the entire concept of friction. Study static and kinetic friction and the difference. I would try and answer your queries, but it would only confuse you more.

It wouldn't roll, it would slide.

This is because you do not understand the entire concept of friction. Study static and kinetic friction and the difference. I would try and answer your queries, but it would only confuse you more.

it won't slide either apparently, that's what the book says. it says it won't move.

Oh and now that you mention static friction, I think u mg cos(o) R is the maximum torque the static friction can provide. so your torque actually ought to be lesser than that sooo u mg cos(o) R > I alpha. 5/2 u mg cos (o) > ma

mg sin (o) - umgcos(o) < 5/2 u mg cos (o).

am I right? thanks! this was a terrible way to die on a problem.

 

[lekh2003]

That is incorrect. Either your book is wrong or you are misinterpreting it.

 

[Vriska]

That's wrong. No friction is needed to make it start moving (sliding). Friction is needed to start it rolling.

A cube is an imperfect sphere. Draw a diagram showing the forces acting on a cube and the conditions that need to make it tip over (aka roll).

okay, I have this cube on an incline , so let's say its start tipping over on one edge with c.m as centre of rotational . you have friction and gravity exerting torques. you have gravity trying to roll a cube with side r on one direction with torque = mgsin(o) r/2. and you have a torque from friction that equals u mg cos(o) r/2 operation in the opposite direction.

to tip mg sin(o) r/2 > umg cos(o) r/2. tan(o) >u and it tips. is this right?

i don't know what about a cube on a table with a force being applied at its top edge horizontally. I take the centre of rotation of to be the bottom edge. I find that it starts tipping when F = mg/2 with no involvement of frictional force. something seems odd :|

 

[Vriska]

That is incorrect. Either your book is wrong or you are misinterpreting it.

Okay, looks like I'm misinterpretating it. It say it never rolls. And now I'm confused again. When it slides don't you have kinetic friction acting on it. that also produces a torque right? I can't see anything to balance that torque.

 

[lekh2003]

Okay, looks like I'm misinterpretating it. It say it never rolls. And now I'm confused again. When it slides don't you have kinetic friction acting on it. that also produces a torque right? I can't see anything to balance that torque.

Kinetic friction opposes the motion, but static friction generates torque. Think about it.

 

[Vriska]

Kinetic friction opposes the motion, but static friction generates torque. Think about it.

I don't get it? kinetic friction opposes motion by exerting a force in the opposite direction right? I'm not sure how there isn't a torque :/

 

[lekh2003]

I don't get it? kinetic friction opposes motion by exerting a force in the opposite direction right? I'm not sure how there isn't a torque :/

Kinetic friction only occurs when there is motion between an object and the ground. It is different from static friction. Static friction is only when the object is static, and in the case of the ball, causing it to tip over.

 

[Vriska]

Kinetic friction only occurs when there is motion between an object and the ground. It is different from static friction. Static friction is only when the object is static, and in the case of the ball, causing it to tip over.

wait if there wasn't the friction = 2/7 tan(o) the sphere starts sliding right? doesn't that motion cause friction and hence rolling??

 

[lekh2003]

wait if there wasn't the friction = 2/7 tan(o) the sphere starts sliding right? doesn't that motion cause friction and hence rolling??

It depends whether you are switching off all friction or only static or kinetic. But remember that rolling ALWAYS needs static friction.

 

[Vriska]

It depends whether you are switching off all friction or only static or kinetic. But remember that rolling ALWAYS needs static friction.

It depends whether you are switching off all friction or only static or kinetic. But remember that rolling ALWAYS needs static friction.

It depends whether you are switching off all friction or only static or kinetic. But remember that rolling ALWAYS needs static friction.

I don't gettit, if I switch off static friction and keep kinetic friction in the case of a sliding sphere on an incline. I'd think it'd do some sliding and some rolling because the friction creates a torque. right?

Also take a cube and put it on a rough surface, and push it from the top with force enough to overcome static friction by not enough to roll over( ie F<mg/2) then what do you think will happen?

 

[haruspex]

if I switch off static friction and keep kinetic friction

Not possible. Suppose you were to push with a force that's enough to overcome static but not kinetic. So it would move, but instantly stop again, then move again... Kinetic can never exceed static.

I had stayed out of this thread because I do not understand the question. An "imperfect sphere" could be any shape at all. Why call it that? Is it only slightly imperfect? All real spheres are.
And as others have commented, it would be nonsense to say that in the absence of friction it would not move. So I strongly suspect we do not yet have the exact problem statement. Perhaps the original is not in English?

 

[Vriska]

Not possible. Suppose you were to push with a force that's enough to overcome static but not kinetic. So it would move, but instantly stop again, then move again... Kinetic can never exceed static.

I had stayed out of this thread because I do not understand the question. An "imperfect sphere" could be any shape at all. Why call it that? Is it only slightly imperfect? All real spheres are.
And as others have commented, it would be nonsense to say that in the absence of friction it would not move. So I strongly suspect we do not yet have the exact problem statement. Perhaps the original is not in English?

no, I read thw question wrong it said it wouldn't roll. Well, idk, I think it should because kinetic friction exerts a torque right?

 

[haruspex]

no, I read thw question wrong it said it wouldn't roll. Well, idk, I think it should because kinetic friction exerts a torque right?

So, to be clear, it says that the sphere starts at rest, and in the absence of friction it will not roll. Is that right?

That would certainly be true for a uniform perfect sphere. It takes a moment about the mass centre to cause the rotation. The weight and normal force both act through the mass centre, so do not create such a torque.
But for an imperfect sphere the normal need not pass through the mass centre, so there could be a torque. It could even start rotating the wrong way.

On the other hand, mere rotation does not constitute rolling. For that, it needs to rotate at exactly the right rate so that the point of contact does not slide, despite the lack of friction.
For a sphere on a level surface, there is a certain height at which a horizontal force would indeed produce rolling. Question is, can the same happen for an imperfect sphere as a result of the normal force?
(My intuition is that it can.)

 

[Vriska]

So, to be clear, it says that the sphere starts at rest, and in the absence of friction it will not roll. Is that right?

That would certainly be true for a uniform perfect sphere. It takes a moment about the mass centre to cause the rotation. The weight and normal force both act through the mass centre, so do not create such a torque.
But for an imperfect sphere the normal need not pass through the mass centre, so there could be a torque. It could even start rotating the wrong way.

On the other hand, mere rotation does not constitute rolling. For that, it needs to rotate at exactly the right rate so that the point of contact does not slide, despite the lack of friction.
For a sphere on a level surface, there is a certain height at which a horizontal force would indeed produce rolling. Question is, can the same happen for an imperfect sphere as a result of the normal force?
(My intuition is that it can.)

OKAY , I'm starting to get it , almost , what happens if there's no friction? It just comes down right , just slides down , but what if there's just little friction - You need u = tan(o ) to break static friction and cause sliding but 2/7 tan(o) for it to start rolling , so if it's less than 2/7tan(o) - It's like there is no friction at all and it starts rolling ?! Seems odd

 

[haruspex]

what happens if there's no friction

That's what I was describing in post #16. If a perfect sphere it will just slide, no rotation. For an imperfect sphere it could anything - just slide; slide with some rotation, maybe even "backwards" rotation; or in a very special case it might roll initially. In the last two cases the rotation will change the circumstances, so then it might do something else.

what if there's just little friction

For a perfect sphere, as you say, there is a threshold of friction above which it will immediately roll (but 2/7 doesn't sound right... 5/7 maybe?). Below that threshold, but nonzero, it will slide and rotate, but never transition to rolling. Where does your μ=tan(θ) come from? That's for a block that cannot rotate, no?

 

[Vriska]

That's what I was describing in post #16. If a perfect sphere it will just slide, no rotation. For an imperfect sphere it could anything - just slide; slide with some rotation, maybe even "backwards" rotation; or in a very special case it might roll initially. In the last two cases the rotation will change the circumstances, so then it might do something else.

For a perfect sphere, as you say, there is a threshold of friction above which it will immediately roll (but 2/7 doesn't sound right... 5/7 maybe?). Below that threshold, but nonzero, it will slide and rotate, but never transition to rolling. Where does your μ=tan(θ) come from? That's for a block that cannot rotate, no?

Okay, I completely get the perfect sphere thing now. thanks!

oh yeah, the tan(o) doesn't belong anywhere.

Now the imperfect sphere, let it be a cube on an incline (maybe what they meant rather than a bulgy one where weird things happen) , so I'd guess it'd only rotate if friction were u >tan(o) right?? I'm not sure but the answer is it won't roll at all.

Edit: nevermind this, I'm getting confused over nothing. thanks for the help though!