# Bicyclist travles in a circle

1. Dec 28, 2004

### Clari

For a bicyclist travels in a circle, I want to ask whether the force of friction exerted by the road provides the centripetal force??

Last edited: Dec 28, 2004
2. Dec 28, 2004

### LENIN

Yes it does.

3. Dec 28, 2004

### Clari

Hi Lenin,
umm....but seems that the force of friction is in different position to the centripetal acceleration. The centripetal acceleration points towards the circle, but friction of the road points tangential to the circle.....so why is that?

4. Dec 29, 2004

### Cyrus

The centripital force is caused by the changing direction of velocity of the biker as he goes around in the circle. The friction acts to keep his tires from slipping as he makes his turn.

5. Dec 29, 2004

### Staff: Mentor

The frictional force points towards the center, thus creating a centripetal acceleration.

6. Dec 29, 2004

### Cyrus

Doc, isint the centripital force caused by the changing direction of the velocity vector of the biker?

7. Dec 29, 2004

### dextercioby

It is.Doc pointed out that in the circular motion of a bicycle/motorcycle,since the vehicle leans towards the center of the circle,the friction force will act on a radial direction but as a centripetal force,havin' the "arrow" towards the center of the circle.This situation looks awkward when compared to the case of linear motion in which the direction of the friction force is the same with the direction of movement (the acceleration vector and the kinetic friction vector have the same support),but that's the case here and it should not surprise anybody.You were right,the friction force keeps the bicycle/motorcycle from slipping.

Daniel.

8. Dec 29, 2004

### Staff: Mentor

I would say it like this: The changing direction of the velocity tells you that the bike is undergoing an acceleration, which must be caused by a force. The force that causes the acceleration is the frictional force acting towards the center.

9. Dec 29, 2004

### Cyrus

Dex, it just seems odd to say that friction causes the acceleration. If a rocket ship in outer space were moving in a circle, there would be a centripital acceleration. But friction would not be the "cause" of it.

Thanks Doc, I like that alot better. :-) It just seemed odd to make friction the cause without mention to a changing direction of velocity.

I also misread the origiona question. I thought he said centripital acceleration, but he said the cause of the centripital FORCE. Sorry, now I see.

Last edited: Dec 29, 2004
10. Dec 29, 2004

### dextercioby

I didn't say that...Let's consider the simple case of a body of constant mass.Then Newton's law
$$\frac{d\vec{p}}{dt}=\sum_{k} \vec{F}_{k}$$ (1)
becomes:
$$m\frac{d\vec{v}}{dt}=\sum_{k} \vec{F}_{k}$$ (2)
,or
$$m\vec{a}=\sum_{k} \vec{F}_{k}$$(3)
,or
$$\vec{a}=\frac{1}{m}\sum_{k} \vec{F}_{k}$$ (4)

Interpret (4) from a logical point of view:
An acceleration of a body is caused by the nonzero vector sum of forces acting on it & A nonzero vector sum of forces acting on the body is caused by an acceleration of the body.

(Kinetic) Friction force is a force.Sorry about the tautology.According to (4) it contributes to the total (resultant) acceleration of the body by the acceleration vector associated with it.That association is made simply dividing the force vector by the body's mass.This means that every force induces an acceleration and viceversa.So the net effect (the acceleration of the body) is a (vector) sum of effects:the gravity effect,the friction effect,the inertial forces effect,the electromagnetic forces effect,and so on...So friction would be the cause of the centripetal acceleration due to friction and viceversa.According to (4),the existence of a centripetal accleration is due to a force.To the friction force in the case of the bicycle/motorcycle,to the Lorentz force in the case of a charged particle in a ring of an accelerator,...

I'm sure u know that in empty space,where's no friction,the gravity force->centripetal acceleration due to gravity and a centripetal acceleration due to gravity->the force of gravity...

Daniel.