Direction of Friction: Rotating a Wheel Up a Hill

[R Power]

I got it. It just struck my mind now! and was so simple.

1.) If I push a wheel then friction helps in rotation by producing torque and my push creates a linear movement (tends to slide the wheel) and together they produce a roll.

2.) If an axle gives torque to wheel, friction provides linear movement and axle provides torque and together they produce a roll.
It was simple.
But Doc ALl confused me:

Friction does two things: It contributes a linear force and a torque.

No my friend I think frictionn will never give both torque and linear force. In the cases above friction either fully provides torque(1.case) or fully provides linear force(2.case). It never does both things. So rethink! u told me that in case 1. friction will give both torque and linear force to wheel , for torque it's ok but how can it give linear forward movement to wheel since it's direction is opp to wheel movement and thus produces torque.However in case of axle providing torque i.e case 2 u were correct , friction will provide linear force but still no torque.

Friction does two things: It contributes a linear force and a torque.

Rethink case 1.

 

[sophiecentaur]

Bearing in mind that a couple (torque) is defined as the product of force times distance, I can't recall any textbooks being fussy about where that force came from!

 

[sophiecentaur]

If there is a ball on a mat, I can pull the mat towards me. The ball will move towards me AND start to rotate. Nicht war?

 

[Doc Al]

first of all let me tell you how i applied force. I simply pushed the wheel. U r confused about top point and bottom point experiencing 10N force i think.
See, a body is made of a number of particles(say infinite), when a body accelerates under effect of a force , each particle of body acc by same amount, that means each particle of body experiences same force. This is what i meant.

If you push an object with 10 N of force that does not mean that each particle of the object experiences 10 N of force.

So the bottom point or particle at bottom or group of particles at bottom and top will also experience a force of 10N.
This is what I meant.

And it still doesn't quite make sense.

Now reconsider my model and tell me if friction can provide any linear force?

All forces contribute to the linear force, including friction.

Bcoz friction is produced due to particles of body at bottom hitting ground due to force i applied to wheel. So friction force equal to 10N and opp in direction is produced.

Friction does not have to equal the force you exert on the bottom of the wheel.

This friction force along with force on particles at top creates a couple.
Now particle(s) at top experienced a force of 10N and same is friction's max instataneous value in opp direction. This creates torque. So there is no friction force left to provide linear motion.
Also in this case friction is in direction opp to wheel's linear movement so why it will provide wheel a linear movement . It will just give torque.
But Doc All said it will provide linear movement.

If you exert 10 N at the top and bottom of the wheel parallel to the surface, you've exerted a net force of 20 N on the wheel. If friction provides 10 N in the opposite direction, then the net force is 20 - 10 = 10 N. That determines the linear acceleration of the wheel's center of mass.

The torque is determined in a similar manner. The two 10 N forces you exert produce 0 net torque. The friction force thus produces the net torque.

I got it. It just struck my mind now! and was so simple.

1.) If I push a wheel then friction helps in rotation by producing torque and my push creates a linear movement (tends to slide the wheel) and together they produce a roll.

Once again, it is the vector sum of all forces on the wheel that determine the linear acceleration of the center of mass.

2.) If an axle gives torque to wheel, friction provides linear movement and axle provides torque and together they produce a roll.
It was simple.

Not that simple. Do not neglect the torque contributed by the friction force.

But Doc ALl confused me:

No my friend I think frictionn will never give both torque and linear force. In the cases above friction either fully provides torque(1.case) or fully provides linear force(2.case). It never does both things.

Nonsense.

So rethink! u told me that in case 1. friction will give both torque and linear force to wheel , for torque it's ok but how can it give linear forward movement to wheel since it's direction is opp to wheel movement and thus produces torque.However in case of axle providing torque i.e case 2 u were correct , friction will provide linear force but still no torque.

Rethink case 1.

I urge you to rethink all of your statements in the light of Newton's laws of motion.

 

[R Power]

OK Doc leave all this(since I've understood) , come to the where we start from , when a wheel rolls up a hill due to torque provided by axle, direction of friction will be up the hill, right??
I think u agreed to me. But in one of my books they have taken it down the hill. Is the book wrong or we are wrong somewhere?

 

[SystemTheory]

A body of mass m and moment of ineria J taken about its central axis rolls down an incline plane with friction limited to the surface contact patch. The body is assumed to be rigid.

Taken in the direction of motion on the plane, the sum of forces acting on the rigid body minus the mass times acceleration equals zero. Let F be the force of resolved gravity and f be the friction, then acceleration is given by:

a = \frac{F-f}{m}

The torque is given by:

T = fr

Angular acceleration about the central axis:

\alpha = \frac{fr}{J}

For a body of mass m, the friction and rates of acceleration are functions of moment of inertia J, so bodies of different inertia have different rates of acceleration down the plane.

Notice a force acting at the center of mass, or at the axis which includes the center of mass, generates zero torque. Also the bearings in a mechanical axle support a force but not a torque. The brakes on such a machine require a structure to couple braking torque to the frame, bypassing the axle, or the brakes would just go round and round with the wheels.

 

[sophiecentaur]

For any of this to work, you need a frame. So why not assume that the wheel is massless and that the frame has the mass. Then we need not consider Moment of Inertia - just forces and mass.
No one seems to have read / understood / responded to my statement that it can all be reduced to levers. The wheel thing just adds confusion.
And you can even forget friction if you drive the car / lever on a rack rather than a friction surface. All the basics will remain the same - the essence shines through.

 

[SystemTheory]

I think the study of bodies rolling downhill is a better approach in terms of common sense. Add a counter-torque acting at the central axis in the equations above, and when F - f = 0 the acceleration a = 0 and rotational acceleration alpha = 0, as when a brake is applied.

The moment of inertia J cannot be eliminated from problems of motion because it absorbs rotational kinetic energy, which takes energy away from the translational rotational energy.

Place a body on a frictionless plane and the initial potential energy U = mgh, or mass times standard gravity times height. The only way to account for the slower exit velocity of rolling bodies is to store energy in the rotational inertia J.

I know inertia complicates the example a bit, but I think R Power is trying to visualize the common sense interpretation of rolling motion in bodies and vehicles, so it is worth the effort to make some case studies based on a traditional dynamic solution framework.

Your frame of reference may have merit, but I'm not sure J can be eliminated except under the assumption of constant velocity, and in downhill motion, that is not the case.

 

[sophiecentaur]

We really need to sort out the model we are discussing.
Is the wheel a wheel on a massless frame or is it a massless wheel on a massive frame? That would be a much better model to study as it is realistic. If we are talking of cars, the wheel MI is negligible, surely.
If there is no friction, the wheel will not rotate in any case and the car will go nowhere - just slipping down the hill, perhaps.
This thread just goes in circles because no one has decided what we're talking about.
There has been some serious nonsense written as a consequence of several misunderstandings, I fear.

 

[rcgldr]

Consider a wheel rolling up the hill by some external force. What will be the direction of friction?

Insufficient information. Is the external force greater than m g sin(θ), where θ is the angle of the hill? You need to know the direction of the net force.

Net force = (external force) - (m g sin(θ))

If the net force is up hill, then the friction force is down hill, if the net force is down hill, then the friction force is up hill. If the net force is zero, then there is no friction force. The direction of the velocity doesn't matter, only the direction of the acceleration.

This ignores rolling resistance which can apply an opposing force and opposing torque at the same time to decelrate a rolling object free of any other forces.

 

[R Power]

If i give a force to a wheel uphill where net force is in uphill direction. That's ok!

But if an axle provides torque to a wheel up hill as if a car moving uphill, then what will bw direction of friction?
I think friction will act uphill i.e in the direction of movement of car.

 

[sophiecentaur]

Of course it will. It's the only force in an uphill direction to make the car go that way. It's a REACTION force - that means it acts against the force causing it. If the (driven) wheel pushes down the hill the car is pushed uphill because of friction. When g dominates and the car runs downhill, the friction force is uphill and slows the car down.

This is all so elementary. Just think about Newton's laws and apply them here, rigorously.

Yet again, I don't think the situation has been described unambiguously and understood by both sides of the argument. Are we talking driven vehicles or trailers? The difference is significant. There is no point continuing until that's cleared up.

 

[R Power]

I just wanted to confirm this only in the beginning and even I don't know where this thread has gone. In one of my books direction of friction on wheels accelerating up is taken downwards, so I thought I may be wrong in my mind and just wanted to confirm. That was all.
And yeah! we were comparing driven vehicles and trailers, !

 

[sophiecentaur]

I just wanted to confirm this only in the beginning and even I don't know where this thread has gone. In one of my books direction of friction on wheels accelerating up is taken downwards, so I thought I may be wrong in my mind and just wanted to confirm. That was all.
And yeah! we were comparing driven vehicles and trailers, !

"Wheels accelerating up"? Driven up or driving up?
That is the whole point. The answer is different for each case.

 

[R Power]

Driven up by axle. No trailer , just like drive wheels of a rear wheel drive car.

 

[sophiecentaur]

Ah well, that appears to be wrong. The force ON the ground is downwards; it has to be for the reaction (friction) force to push the car uphill.

 

[SystemTheory]

R Power
system theory
consider the case of a wheel going up the hill.
Though i understand the case of wheel rolling down, direction of friction clearly.
What i am asking is : When wheel rolls down firction produces torque and thus rotation and there is a downward motion due to gravity which together with rotation creates a "roll".That's clear .OK.
But when wheel goes up especially wheel on an axle , torque is provided by axle , friction just counter acts to oppose that torque in uphill direction, then what provides linear motion to wheel to roll instead of rotate.
In previous case gravity provided linear motion and friction provided rotation and togehter they both created rolling motion.
But in later case where does linear motion come from?
ReAD CAREFULLY!

This sketch shows the rear arm of a shaft powered motorcycle. For simplicity let all torques and forces act on the rear wheel. If the resolved weight for F acts to the right (downhill) a braking torque must be applied (reaction friction force f acts uphill) such that velocity is constant. Thus the motorcycle is either at rest or at constant velocity with F = f.

I hope this picture is "worth a thousand words" as far as the confusion on this thread.