Direction of static friction while rolling

[arunbg]

In my physics textbook (Resnick, Halliday, Walker) , it is given that the direction of force of static friction acting on a wheel undergoing pure rolling without sliding on the ground and whose centre of mass is accelerating uniformly, is the same as the direction of acceleration of COM.

However when a ball sliding down a ramp is considered, the direction is given opposite to the acceleration( up the ramp) , the reason given that the wheel has a tendency to slide down the ramp and friction must oppose this tendency.

I find that the first scenario is only a generalisation of the second with a=g . But then why is the direction of friction different?
Or is one of these assertions wrong ?

 

[Doc Al]

Both assertions are correct. In the first case, the friction is the cause of the (translational) acceleration. In the second case, gravity provides the accelerating force while the friction reduces the net force (as it also provides a torque to keep the ball rolling).

Note that in both cases the friction opposes slipping between the surfaces. In the first case, the wheel surface would slip towards the rear without sufficient friction towards the front opposing it. In the second case, the ball surface would slip forwards if it didn't rotate, thus the friction must act towards the rear to oppose it.

 

[arunbg]

Hmm, So Doc you mean that in the first case friction is actually causing the translational motion and moves the COM and rotation of the wheel is basically due to the external force ? Could you please clarify case 1 a bit more?

THanks for the reply.

 

[Doc Al]

I assume that the rolling wheel is not being pulled by any other external force. In order for it to accelerate, there must be an external force acting on it; that external force is the friction of the road on the wheel.

Picture a car trying to accelerate. If there were no friction, you could press on the gas pedal all day and still not change the car's velocity. It requires an external force to accelerate.

 

[arunbg]

Ok now I get it, so you mean to say that the rotation of the wheel is internal while friction translates.This wasn't given in the book clearly and so I got confused.

Thanks a lot Doc

 

[Doc Al]

Ok now I get it, so you mean to say that the rotation of the wheel is internal while friction translates.

I'm not saying that at all. Friction exerts a force on the wheel; that force also produces a torque.

 

[arunbg]

Ok so friction translates forward and slows down rotation due to internal force ,right?

 

[Doc Al]

That sounds better.

But the main thing to take away from this discussion is that friction always acts to prevent slipping between surfaces. So if you can figure out which way the surfaces are trying to slip, you can easily determine the direction of the friction force.

 

[arunbg]

thanx doc Al

 

[elabed haidar]

doc al i still can't understand why the direction of friction on a straight road is with the direction of motion of the principle of preventing sliding on a straight road hard

 

[Doc Al]

doc al i still can't understand why the direction of friction on a straight road is with the direction of motion of the principle of preventing sliding on a straight road hard

State the exact situation you are trying to understand. Is there acceleration?

 

[elabed haidar]

okay forget what i said my question is
about the rolling i need to know the difference between sliding and non sliding if an inclined plane and a horizontal plane aand how should i act at each problem?

 

[elabed haidar]

my second question is in an inclined plane what is the relation between the coefficent of static friction and kinetic friction i heard that if the coefficent i get is less than the coefficent of the static coefficent given it is called kinetic how is that

 

[Doc Al]

okay forget what i said my question is
about the rolling i need to know the difference between sliding and non sliding if an inclined plane and a horizontal plane aand how should i act at each problem?

Assuming something--a cylinder say--is rolling without slipping, then the only friction involved will be static friction.

If the cylinder is just rolling down a hill (nothing pulling it but gravity), then the friction acts in the opposite direction of the motion. If it's rolling along a horizontal surface, then the speed is constant and there's no friction required. (At least in the ideal case.)

To figure out the amount of static friction in the first case, you'd need to apply Newton's laws.

When sliding is involved, then you have kinetic friction. Kinetic friction can be calculated using μN.