Why Does Friction Act Towards the Center in Circular Motion?

[Gunman]

Homework Statement

A car is traveling along a circular route. There are three forces acting on it. 1)Normal force. 2) Weight. 3)Frictional force. I don't understand how come the frictional force acts towards the centre of the circle? Frictional force is supposed to oppose motion. So how come its towards the centre of the circle? Ya. Thanks for the help. =)

Homework Equations

The Attempt at a Solution

 

[nrqed]

Homework Statement

A car is traveling along a circular route. There are three forces acting on it. 1)Normal force. 2) Weight. 3)Frictional force. I don't understand how come the frictional force acts towards the centre of the circle? Frictional force is supposed to oppose motion. So how come its towards the centre of the circle? Ya. Thanks for the help. =)

Homework Equations

The Attempt at a Solution

It's a common misconception that friction force opposes the motion. This is not true. Actually, when you walk, the friction force on your shoes is in the *same* direction as your motion!

In uniform circular motion, the net force must be toward the center of the circle. The only force that may be in that direction here is the friction force. (it makes sense...if there is no friction force, a car cannot take a curve (if the surface is flat), the car will "fly out" of the curve)

 

[bel]

|gravity |= |normal|
so they cancel out

so, the centripetal force equals the frictional force (acting sideways on the tires) So friction is normal force times the co-efficient of kinetic friction, and the centripetal force is (mv^2)/r. The mass of both sides of the equation cancels out, leaving g*co-efficient = (v^2)/r. You have to know at least two of the three variables to find the last, of course, and that's the solution if the circular route is not a banked curve.

 

[Gunman]

Hm.. nrqed. I understand why you say that frictional force is same direction. Bt why then convectionally in a free body diagram the frictional force acting on a body is drawn opposite to the direction of motion?

 

[nrqed]

Hm.. nrqed. I understand why you say that frictional force is same direction. Bt why then convectionally in a free body diagram the frictional force acting on a body is drawn opposite to the direction of motion?

Not always, no. It depends a lot on the situation!

For example, consider the following case which involves motion along a straight line instead of circular motion. You have a block of mass m on top of a block of mass M. Someone pushes on the lower block (M) in such a way that the two blocks are accelerating without the top block sliding. If you draw the free body diagram of the top block (of mass m), you will have a situation where the static friction force is in the same direction as the motion of the block.

The upshot is that it is simply not always true that friction is opposite to the motion. And as the example I just mentioned showed, you may even have motion and yet have a *static* friction force involved!

But one thing *is* true. A kinetic friction force will indeed always be opposite to the motion relative to the surface on which the object is moving. *That* is true but it can actually be subtle. I won't go into that for now.

As for static friction force, the rule of thumb to find the direction is to ask the following: imagine that friction would be completely removed, in what direction would the object slip (it's not always obvious what the answer is but let's assume that the answer is obvious). Then the static friction force will be opposite to that. In the case of the car in UCM )on a flat surface, not a banked one), then it is clear that if the road is completely icy, the car will move away from the center. So the static friction force in toward the center. But again, another argument is that there must be a net force toward the center in UCM and the only force available for that here is the static friction force.

Hope this helps a bit.

 

[Gunman]

Thanks man. =) haha..Think I got a clearer picture of friction. =)

 

[nrqed]

Thanks man. =) haha..Think I got a clearer picture of friction. =)

You are welcome!

A last example, with kinetic friction this time, to show that even that can be in the same direction as the motion.

Let's say you pull to the right on block M (the bottom one) very abruptly so that block m does slide relative to block M (for a very short time).
Now, during that brief period, block m will be moving to the right (relative to th eground) but it will be sliding *left* relative to the surface on which it is in contact, that its the top of block M . So the kinetic friction force wil be to the right!


I am glad I could help a bit. Finding the direction of friction forces is very subtle but unfortunately books usually just show the simplest examples which do not show all the subtleties involved!

Bets luck