Rolling without slipping down an inclined plane

[dyn]

Hi
If a rigid disc rolls down an incline plane without slipping then the component of weight down the plane causes the disc to accelerate downwards but the frictional force causes a torque which causes the disc to rotate, At the point of rolling without slipping the velocity of the centre of mass is equal to Rω. Hopefully I'm right so far ? Now comes the part where I'm confused.
When rolling without slipping the point of the disc in contact with the plane is instantaneously at rest so the frictional force is zero. This means the torque is now zero and so the angular speed of rotation must remain constant. Is this correct ?
If this is correct this this must mean the velocity of the centre of mass which is still accelerating must become greater than Rω so the disc must start to slip again ?
This seems to imply the rolling without slipping condition cannot be maintained which seems wrong. Where am i going wrong ?
Thanks

 

[Dale]

the point of the disc in contact with the plane is instantaneously at rest so the frictional force is zero

This is not correct. The frictional force is non-zero. Remember there is static friction and dynamic friction. This is static friction.

 

[dyn]

Is it static friction that causes the torque on the disc ?

 

[dyn]

When the disc initially starts to slide (before it starts to roll) is it not kinetic friction that causes the torque on the disc ?

 

[Dale]

Is it static friction that causes the torque on the disc ?

Yes.

When the disc initially starts to slide (before it starts to roll) is it not kinetic friction that causes the torque on the disc ?

If it rolls without slipping then it is, by definition, using static friction.

 

[dyn]

If it is given a push initially down the plane then initially it will slide , so at this time the point of the disc in contact with the plane is moving relative to the plane . so this must be kinetic friction ?

 

[PeroK]

If it is given a push initially down the plane then initially it will slide , so at this time the point of the disc in contact with the plane is moving relative to the plane . so this must be kinetic friction ?

Only if it slips. Imagine you push your bike. The tyres don't slip. Static friction acts (immediately) and the wheel rolls without slipping.

 

[Dale]

If it is given a push initially down the plane then initially it will slide , so at this time the point of the disc in contact with the plane is moving relative to the plane . so this must be kinetic friction ?

Usually not. Again, the term rolling "without slipping" (which you used 5 times in your original post) means that you are using static friction not kinetic friction. There is no reason whatsoever that rolling must begin with slipping.

In fact, in most ordinary circumstances rolling will begin with static friction (without slipping) and will continue with static friction (without slipping). You could force rolling to begin with kinetic friction, but it would require something weird like "peeling out" or starting with your brakes applied and beginning movement with an external push. It can be done, but it would be unusual.

Usually it will not initially slide, and (by definition) it does not slide if it is rolling "without slipping" as you repeatedly specified.

 

[PeroK]

... one example where motion starts with slipping is a snooker ball. Depending on how it's cued it will slip along the cloth until kinetic friction induces rolling without slipping.

 

[Dale]

... one example where motion starts with slipping is a snooker ball. Depending on how it's cued it will slip along the cloth until kinetic friction induces rolling without slipping.

Yes, in this case the large externally applied force is very important.

 

[dyn]

... one example where motion starts with slipping is a snooker ball. Depending on how it's cued it will slip along the cloth until kinetic friction induces rolling without slipping.

So in this case kinetic friction causes a torque on the ball. But when it is rolling without slipping that is caused by static friction ?

 

[jbriggs444]

So in this case kinetic friction causes a torque on the ball. But when it is rolling without slipping that is caused by static friction ?

Yes. I would say that the not slipping is "maintained" by static friction.

 

[Dale]

But when it is rolling without slipping that is caused by static friction ?

Yes, by definition.

 

[dyn]

When analysing rolling without slipping conservation of mechanical energy can be used. This means the static friction does no work. Is this because the point of contact of ball/disc is not moving relative to the surface ?

 

[Dale]

When analysing rolling without slipping conservation of mechanical energy can be used. This means the static friction does no work. Is this because the point of contact of ball/disc is not moving relative to the surface ?

Yes, in this case.

It is possible for static friction to do work in certain other scenarios, but mechanical energy can still be used in those as well. In those scenarios it can be used because even though static friction does work it does not dissipate energy, meaning energy is not converted to any other non-mechanical form.

 

[dyn]

Yes, in this case.

It is possible for static friction to do work in certain other scenarios, but mechanical energy can still be used in those as well. In those scenarios it can be used because even though static friction does work it does not dissipate energy, meaning energy is not converted to any other non-mechanical form.

In the cases where static friction does work , is conservation of energy used in the form that the change in KE+PE is equal to the work done by static friction ?

 

[Dale]

In the cases where static friction does work , is conservation of energy used in the form that the change in KE+PE is equal to the work done by static friction ?

If that is the only force doing work, yes. If you have multiple forces doing work then the change in KE+PE would be equal to the sum of those works.

 

[Ehyeh Asher Ehyeh]

"When rolling without slipping the point of the disc in contact with the plane is instantaneously at rest so the frictional force is zero."
There is nothing static about it; the disc is undergoing both linear and angular acceleration the entire time due to Gravity.

 

[jbriggs444]

"When rolling without slipping the point of the disc in contact with the plane is instantaneously at rest so the frictional force is zero."
There is nothing static about it; the disc is undergoing both linear and angular acceleration the entire time due to Gravity.

For the purposes of the term "static friction", all that is required is that the mating points of contact are momentarily at rest with respect to one another -- that their relative velocity is zero.

 

[Dale]

There is nothing static about it

The friction is static friction.

 

[Ehyeh Asher Ehyeh]

"Static friction is a force that keeps an object at rest. It must be overcome to start moving the object. Once an object is in motion, it experiences kinetic friction. If a small amount of force is applied to an object, the static friction has an equal magnitude in the opposite direction."~http://www.softschools.com/formulas/physics/static_friction_formula/30/
The Disc is not at rest in any way. The force of the friction however is constant, but not static.

 

[Bandersnatch]

The Disc is not at rest in any way.

What is the linear velocity between the disc and the surface at the point of contact then?

 

[Ehyeh Asher Ehyeh]

What is the linear velocity between the disc and the surface at the point of contact then?

It's whatever the angular velocity translates into at any time-T. Static friction refers to an object at rest on a surface, not a rolling object across a surface. A constant value for friction does not make it a situation of Static Friction.

 

[Bandersnatch]

It's 0, actually. If the two surfaces are not moving w/r to one another along the plane of contact, as is the case when the disc and the incline momentarily touch, then any friction between them is static friction.

 

[A.T.]

Static friction refers to an object at rest on a surface, not a rolling object across a surface.

Wrong. "Static" refers to the relative motion of the contact patches.

 

[weirdoguy]

A constant value for friction does not make it a situation of Static Friction.

But no one said that it's static friction because it has constant value. Kinetic friction also has constant value.

 

[Ehyeh Asher Ehyeh]

"For many dynamics problems, rolling without slipping means there is a friction force acting on the wheel at the contact point P. This friction force prevents slipping. In this instance the friction is known as static friction since there is no relative sliding between the wheel and surface at the contact point P."~https://www.real-world-physics-problems.com/rolling-without-slipping.html
I'll go away now.

 

[Ehyeh Asher Ehyeh]

But no one said that it's static friction because it has constant value. Kinetic friction also has constant value.

The whole debate was about parsing terms and I recognize the convention now and surrender the point. I'd hate myself if I were unconventional.

 

[Dale]

"Static friction is a force that keeps an object at rest. It must be overcome to start moving the object. Once an object is in motion, it experiences kinetic friction. If a small amount of force is applied to an object, the static friction has an equal magnitude in the opposite direction."~http://www.softschools.com/formulas/physics/static_friction_formula/30/
The Disc is not at rest in any way. The force of the friction however is constant, but not static.

I am sorry to hear that you are learning physics from such a bad reference. This statement is incorrect.

Static friction is a force that keeps two surfaces from slipping. It must be overcome to start slipping at the surfaces. Once the surfaces are slipping, it experiences kinetic friction. If a small amount of net force is applied to an object in a direction tangent to the surface, the static friction has an equal magnitude in the opposite direction.

This site uses similar terminology to mine: https://www.khanacademy.org/science...s/inclined-planes-friction/a/what-is-friction
Note the term "relative motion" here, which is the same as slipping: http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html
Wikipedia also uses the term "relative motion": https://en.wikipedia.org/wiki/Friction#Static_friction
This says "sliding" instead of "slipping": https://www.sciencedirect.com/topics/engineering/static-friction
This one also says "slide": http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/ben_townsend/staticandkineticfriction.htm

 

[Ehyeh Asher Ehyeh]

I am sorry to hear that you are learning physics from such a bad reference. This statement is incorrect.

Static friction is a force that keeps two surfaces from slipping. It must be overcome to start slipping at the surfaces. Once the surfaces are slipping, it experiences kinetic friction. If a small amount of net force is applied to an object in a direction tangent to the surface, the static friction has an equal magnitude in the opposite direction.

This site uses similar terminology to mine: https://www.khanacademy.org/science...s/inclined-planes-friction/a/what-is-friction
Note the term "relative motion" here, which is the same as slipping: http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html
Wikipedia also uses the term "relative motion": https://en.wikipedia.org/wiki/Friction#Static_friction
This says "sliding" instead of "slipping": https://www.sciencedirect.com/topics/engineering/static-friction
This one also says "slide": http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/ben_townsend/staticandkineticfriction.htm

I never misunderstood that Partner.

 

[PeroK]

"For many dynamics problems, rolling without slipping means there is a friction force acting on the wheel at the contact point P. This friction force prevents slipping. In this instance the friction is known as static friction since there is no relative sliding between the wheel and surface at the contact point P."~https://www.real-world-physics-problems.com/rolling-without-slipping.html
I'll go away now.

Just to add a point:

If the wheel is accelerating or decelerating (in the case of rolling without slipping), then a non zero static friction force acts. If the wheel is rolling at constant speed, on a horizontal surface, then no friction acts. To see this, simply consider the wheel moving with constant angular momentum about its centre. No external force is needed to maintain this.

 

[dyn]

Some of the above posts seem to mirror my confusion. When a ball/disc slides down an incline plane , the point of contact is moving relative to the surface so the external torque that causes the ball/disc to start rotating is kinetic friction. At the instant the rolling without slipping condition is met the kinetic friction instantaneously changes to static friction. That seems to be correct but it also appears a bit strange.
Also if the ball/disc is accelerating for a long time , then static friction force might not be enough to keep up with the linear speed so the ball/disc could start sliding again ?

 

[jbriggs444]

Some of the above posts seem to mirror my confusion. When a ball/disc slides down an incline plane , the point of contact is moving relative to the surface so the external torque that causes the ball/disc to start rotating is kinetic friction.

Yes. If one begins with the ball already moving but not turning fast enough [or too fast], it must be sliding and the relevant force is kinetic friction.

At the instant the rolling without slipping condition is met the kinetic friction instantaneously changes to static friction. That seems to be correct but it also appears a bit strange.

Yes, it is correct.

Also if the ball/disc is accelerating for a long time , then static friction force might not be enough to keep up with the linear speed so the ball/disc could start sliding again ?

The coefficient of static friction is generally larger than the coefficient of kinetic friction. For an inclined plane with contant slope, if kinetic friction is more than enough to keep up with the acceleration then static friction is also sure to be more than enough.

 

[Ehyeh Asher Ehyeh]

I believe the convention is to use the term ‘Static Friction’ for a rolling situation like this. It doesn’t matter how you parse the terms as long as you understand so you can solve the problem.
This is an idealized situation where the angular and linear accelerations are constant, so don’t worry about reality because that would be ‘engineering’ and not physics.
It was a fun post anyway, so thanks for that much!

 

[jbriggs444]

I believe the convention is to use the term ‘Static Friction’ for a rolling situation like this.

It is more than convention.

Microscopically, the mating surfaces are not moving relative to one another. They can settle into place and form a somewhat more solid "grip" than surfaces that are sliding across one another. That is precisely the difference between static and kinetic friction.

The models of static and kinetic friction in terms of $\mu_k$ or $\mu_s$ times normal force are engineering approximations. Not basic physical principles.