# Paradox pure rolling and friction

1. Mar 5, 2013

### persia7

suppose a rigid ball roll on a rigid level with constant velocity , the friction on the contact surface decrease the forward velocity but increase angular velocity ,
how do you explain this paradox?

2. Mar 5, 2013

### Staff: Mentor

Why do you think there is a paradox?

3. Mar 5, 2013

### Staff: Mentor

If the ball really rolls (without slipping), I don't see how this could happen. If the ball is slipping initially, it is possible.

4. Mar 5, 2013

### Staff: Mentor

That's what I assumed.

The classic exercise is for a bowling ball thrown with some velocity onto a lane: calculate the final velocity once it rolls without slipping.

5. Mar 5, 2013

### persia7

because increasing the angular velocity means increase forward velocity,this is paradox!!

6. Mar 5, 2013

### Staff: Mentor

Not necessarily. Realize that the ball is slipping along the surface. It is not rolling without slipping.

Imagine the ball is moving to the right with some initial speed V. It is not rotating. When dropped onto the surface, friction acts to the left. That friction force does two things: It creates a translational acceleration that reduces the ball's translational speed and it creates a rotational acceleration that increases the ball's angular speed.

7. Mar 6, 2013

### persia7

if you are right, it is impossible that there is a pure rolling in world , isnt it paradox!!

8. Mar 6, 2013

### Staff: Mentor

What do you mean by "pure rolling"?

9. Mar 6, 2013

### persia7

in pure rolling velocity of ball and surface at contact point is equal.

10. Mar 6, 2013

### Staff: Mentor

In that case, pure rolling exists.

11. Mar 6, 2013

### Staff: Mentor

What you are calling "pure rolling" is what I usually see called "rolling without slipping". That is certainly possible.

For an example of rolling without slipping in which friction opposes the forward velocity as it increases the angular velocity, just roll the ball down an incline. (Of course, gravity also acts.)

12. Mar 7, 2013

### persia7

i said the velocity is constant . but you say the ball is accelerated , is it paradox?

13. Mar 7, 2013

### Staff: Mentor

Sounds like you are creating impossible conditions, not a paradox. If friction is acting, how can the velocity be constant?

An example of rolling without friction at constant velocity (at least approximately) would be a ball rolling along on a horizontal surface. In that case there is no (static) friction and the ball just keeps rolling. (Of course in real life there would be deformation and energy loss.)

I'm still not sure of what situation you have in mind, so please try again to give an example.

14. Mar 12, 2013

### jack action

If a ball rolls, it needs friction, doesn't it? Otherwise it would only be spinning in one spot without ever going forward (like you need friction between the sole of your shoe and the ground to go forward). If there is friction, then there must be a relative motion between the ball and the ground, hence it must be slipping (even if it is a very small amount).

So I would think that pure rolling without slipping cannot exist if friction is involved. Am I wrong?

15. Mar 12, 2013

### AlephZero

If the center of mass of the wheel is moving with constant velocity, and the wheel is rotating at the correct speed for rolling without slipping, there is no friction force required.

Think about a car travelling a constant speed if there is a stretch of ice on the road (ignoring air resoistance, etc). The wheels will continue to roll without slipping across the ice.

Of course if the speed of the car changes, you need to apply a torque to the wheels to change their rotation speed. But that torque doesn't have to involve friction forces. For example, imagine a rocket propelled car, with a small motor just powerful to spin the wheels up to the correct speed, but not powerful enough to create any friction force to accelerate the car.

16. Mar 13, 2013

### Staff: Mentor

It needs friction (or some other force) to accelerate, but it does not need friction to move at a constant velocity.

No.
You are.