Direction of Friction in Rolling Objects

[whoareyou]

Homework Statement

A forward force on the axle accelerates a rolling wheel on a horizontal surface. If the wheel
does not slide the frictional force of the surface on the wheel is:

A. zero
B. in the forward direction
C. in the backward direction
D. in the upward direction
E. in the downward direction

Homework Equations

N/A

The Attempt at a Solution

The answer key says that the answer is D. My textbook shows a diagram indicating that the answer is B. A similar question online says that answer should be "in the backwards direction (and does zero work on the wheel)." Which one is it?

I'm inclined to go with B because that's what the diagram in my textbook looks like (ie. on a horizontal surface, if the wheel is accelerating forward, static friction acts forward as well at the bottom of the wheel).

But then there's the case where the wheel is rolling down an incline. Then the acceleration is down the incline but the static frictional force is up the incline which is different from the previous situation.

Maybe I don't understand this concept very well, can someone explain?

 

[Doc Al]

A forward force on the axle accelerates a rolling wheel on a horizontal surface.

Note that it is a force on the axle that is accelerating the wheel forward. (I picture the wheel as freely rotating about the axle.)

The answer key says that the answer is D.

That's pretty wacky!

My textbook shows a diagram indicating that the answer is B. A similar question online says that answer should be "in the backwards direction (and does zero work on the wheel)." Which one is it?

Ask yourself: Which way must the wheel turn? What force is available to turn it?

 

[whoareyou]

The wheel should be turning clockwise, so friction should be acting forwards? This is what the diagram looks like in my textbook. But I don't know how to explain any of it using physics!

 

[Doc Al]

The wheel should be turning clockwise, so friction should be acting forwards?

Which direction is it moving? Right or left?

 

[whoareyou]

I'm interpreting forward to be to the right.

 

[Doc Al]

I'm interpreting forward to be to the right.

Good. In which case the wheel will turn clockwise, so what force is exerting that clockwise torque? What direction must friction point to exert a clockwise torque?

 

[whoareyou]

If the wheel is accelerating due to that applied force, then there is also angular acceleration provided from that force. There is also static friction from the ground. So since the net torque vectors and acceleration vectors point in the same direction, then at the bottom, friction has to be pointing backwards (ie. to the left). Except in the diagram in my book, the acceleration is forward, the wheel is rotating clockwise but the static friction force is also forward ...

 

[haruspex]

If the wheel is accelerating due to that applied force, then there is also angular acceleration provided from that force. There is also static friction from the ground. So since the net torque vectors and acceleration vectors point in the same direction, then at the bottom, friction has to be pointing backwards (ie. to the left). Except in the diagram in my book, the acceleration is forward, the wheel is rotating clockwise but the static friction force is also forward ...

The 'forwards' answer is for the case where a torque is applied at the axle, not a forwards force. The diagram doesn't make it clear which case this is. Does that diagram definitely go with this question text?

 

[whoareyou]

No. This is just a diagram from my textbook, not for the question. I thought that it might relate to the question though since a force is applied at the axle, the com is accelerating and the wheel is moving cw. In this diagram, the static friction is forward so I thought this could give some insight to the answer for this multiple choice question.

Btw, if the axle is the axis of rotation then how can you apply a torque there (ie. aren't all points but the points on the axis of rotation rotating?)?

 

[rcgldr]

A forward force on the axle accelerates a rolling wheel on a horizontal surface. If the wheel does not slide the frictional force of the surface on the wheel is ...

Assuming the problem statement is correctly worded, there is a forwards force, not a torque, applied at the axle, resulting in the forwards linear acceleration of the wheel. In this case, the surface exerts a backwards force onto the wheel. The surface friction force is equal to the angular acceleration of the wheel times the angular inertia of the wheel divided by the radius of the wheel.

 

[whoareyou]

In the diagram, it too has a forwards linear acceleration as well, but why the friction force points forwards as well? Why is the situation in the question different than what is being depicted in the diagram?

 

[rcgldr]

Why is the situation in the question different than what is being depicted in the diagram?

The diagram is in conflict with the problem statement. The diagram shows a forwards acceleration at the axle (noted as COM = center of mass) which I assume corresponds to a force (not a torque). The diagram then shows the forwards force that the wheel exerts onto the surface, but the problem statement is asking for the direction of the force that the surface exerts onto the wheel (these are a pair of Newton third law forces).

 

[Doc Al]

If the wheel is accelerating due to that applied force, then there is also angular acceleration provided from that force. There is also static friction from the ground. So since the net torque vectors and acceleration vectors point in the same direction, then at the bottom, friction has to be pointing backwards (ie. to the left).

Exactly.

Except in the diagram in my book, the acceleration is forward, the wheel is rotating clockwise but the static friction force is also forward ...

In this diagram, the only force shown is that due to friction. So we are to assume that is is the friction which is the external force driving the wheel forward. (As would be the case when a torque is applied to the axle, as haruspex said.) This is different than the problem you described.

 

[haruspex]

The diagram is in conflict with the problem statement. The diagram shows a forwards acceleration at the axle (noted as COM = center of mass) which I assume corresponds to a force (not a torque).

I suspect that orange arrow is only showing acceleration, neither a force nor a torque.

 

[whoareyou]

So then I was wrong to assume that since there is an linear acceleration on the com then there is a force acting on the com?

 

[rcgldr]

So then I was wrong to assume that since there is an linear acceleration on the com then there is a force acting on the com?

Going back to the problem statement: "A forward force on the axle accelerates a rolling wheel on a horizontal surface." (a forward force is not a torque). Is this the original problem statement? If not, what is the original problem statement?

 

[whoareyou]

Sorry, I was referring to the diagram.

Also,

The 'forwards' answer is for the case where a torque is applied at the axle, not a forwards force.

How do you apply a torque to the axle instead of a force? Is that done by, instead of pushing on the axle, you rotate the axle?

 

[haruspex]

How do you apply a torque to the axle instead of a force? Is that done by, instead of pushing on the axle, you rotate the axle?

Yes. That's how the driving wheels operate on a vehicle, be it a car, a bicycle or whatever. The non-driving wheels operate the other way: they are pushed forwards linearly by the vehicle. During acceleration, the friction with the road is forwards on the driving wheels but backwards on the non-driving wheels.

 

[whoareyou]

So I tried to draw some free body diagrams for the various situations. Do they look alright? Also, for the third case with a force and a torque which we haven't discussed, what direction would the frictional force point? Or does it depend on the magnitude of the force?

http://i.imgur.com/gwTZElp.png

 

[haruspex]

So I tried to draw some free body diagrams for the various situations. Do they look alright? Also, for the third case with a force and a torque which we haven't discussed, what direction would the frictional force point? Or does it depend on the magnitude of the force?

http://i.imgur.com/KJgmyIu.png

They're right for the scenario that we've been discussing, namely, the wheel is accelerating in the forward direction. In the third diagram the friction can go either way. You can do this yourself as an exercise: Let the linear acceleration be a, the angular acceleration α, and the radius r. Write out three equations:
- one just involving a, α and r
- the torque equation about the axle (I, α, τ, f_s, r)
- the linear force equation (m, a, F, f_s)
Then eliminate a and α between them to get an expression for f_s.

 

[Doc Al]

So I tried to draw some free body diagrams for the various situations. Do they look alright? Also, for the third case with a force and a torque which we haven't discussed, what direction would the frictional force point? Or does it depend on the magnitude of the force?

http://i.imgur.com/gwTZElp.png

In your second diagram, why are two forces shown at the contact point with the ground? There should only be friction.

 

[haruspex]

In your second diagram, why are two forces shown at the contact point with the ground? There should only be friction.

I interpreted them as action and reaction - the forward force from ground on wheel and the backward force from wheel on ground.

 

[Doc Al]

I interpreted them as action and reaction - the forward force from ground on wheel and the backward force from wheel on ground.

That would apply to all three diagrams, not just the second. (And would be quite confusing!)

 

[whoareyou]

My understanding is that the force providing the torque moves around the rim of the wheel. Since the wheel is moving clockwise, the force is pointing to the left at the contact point. But since the contact point cannot be moving relative to the surface, the static frictional force has to act in the opposite direction to prevent slipping.

 

[Doc Al]

My understanding is that the force providing the torque moves around the rim of the wheel. Since the wheel is moving clockwise, the force is pointing to the left at the contact point. But since the contact point cannot be moving relative to the surface, the static frictional force has to act in the opposite direction to prevent slipping.

On a free body diagram of the wheel, only external forces and torques should appear. The only external force in your second diagram is the frictional force from the ground, which gives the wheel its translational acceleration.

The diagram from your book has it correct (though they do not show the applied torque).

 

[MathewsMD]

Hi,

Just reading this thread and I'm a little confused. So is frictional force directed upwards like the answer says or is it backwards (opposite to the direction of motion)?

 

[haruspex]

Hi,

Just reading this thread and I'm a little confused. So is frictional force directed upwards like the answer says or is it backwards (opposite to the direction of motion)?

For the problem as given in the OP, the frictional force is horizontal, in the opposite direction to the applied force. The diagram later posted does not relate to the actual question.

 

[PeroK]

A few experiments you can do with your bicycle:

1. Lock the brakes and try to push the bike along. Quite a lot of friction!

2. Release the brakes. The friction on the ground now produces a backwards force that becomes a torque on the wheel causing it to spin and the bike to move with little effort. So, there's a big difference between "rolling resistance" that includes an element of friction between the tyres and the ground and the usual frictional reistance to sliding.

3. Get on and apply the pedals. The back wheel starts pushing backwards into the ground. The resisting force to this pushes the bike forwards. The mechanics are similar to walking, given that the tyres are slightly flattened against the ground. The difference, of course, is that there is a nett torque on the back wheel, so it's spinning, hence the bike is rolling rather than sliding along the ground. The front wheel is still rolling as when you were pushing the bike.

4. The back wheel will actually be slipping slightly (think of what would happen on ice). So, the forward motion will not quite equal the angular motion of the tyre.

 

[haruspex]

there's a big difference between "rolling resistance" that includes an element of friction between the tyres and the ground and the usual frictional resistance to sliding.

I couldn't understand that sentence. What were you trying to say?
Rolling resistance arises not from friction but from deformation of the tyre and/or wheel under load. The force during compression exceeds the force during decompression, so work is lost. There will also be some frictional losses in the axle.

 

[PeroK]

Just that the total rolling resistance (which probably includes a small element of friction due to slippage) is much less than sliding friction. So, if the bike is moving and you are not pedalling, there is very little friction involved.

 

[Nyhm]

I have a question that seems to best fit into this thread.

I'm only concerned with the direction of friction. I believe that as you accelerate down the road the fs is forward for the wheels subjected to torque and backwards for the wheels being 'pushed'. If i have that right then my question is when the brakes are applied and assuming there is not any slipping (the car gradually slows down) are the forces of friction switched? Meaning, do the tires under torsion have a frictional force opposing the velocity of the vehicle?

 

[NoPoke]

The directions of the forces associated with friction between a pair of surfaces always acts to reduce the relative motion between the two surfaces. To apply this to a situation where there is no slip imagine the motion that would take place if friction between the two surfaces was zero.

 

[Doc Al]

I have a question that seems to best fit into this thread.

I'm only concerned with the direction of friction. I believe that as you accelerate down the road the fs is forward for the wheels subjected to torque and backwards for the wheels being 'pushed'. If i have that right then my question is when the brakes are applied and assuming there is not any slipping (the car gradually slows down) are the forces of friction switched? Meaning, do the tires under torsion have a frictional force opposing the velocity of the vehicle?

Yes, you are correct.