# Friction during pure rotation

But I still have the following problem:

• On one hand I've been told that if pure rotation takes place then the object goes on forever. This must imply no frictional force in any form acting on the body.

• On the second hand I've been told that during pure rotation(no external forces like wind) on a plane surface friction acts opposite to velocity of center of mass (accompanied by change of normal) and slows it down.

Both seem logical enough:
The point of contact doesn't slip therefore no friction is required; So no retarding force and it must go on.
Things don't go on forever; Friction must be present to slow it down.

So, which hand is correct? Or is there a third hand altogether?

• You appear to be confusing friction and rolling resistance. Feb 8, 2018 at 18:14
• Hint: A realistic wheel is not completely rigid. Feb 8, 2018 at 18:15
• Possible duplicate of Rolling resistance and static friction Feb 8, 2018 at 18:19
• @SmarthBansal...You can see that the friction here presents the torque necessary for rolling...If you do that in a frictionless plane , then the wheel will only slide,not rotate...Friction here is not dissipative... Feb 8, 2018 at 18:27
• Feb 8, 2018 at 18:27

Both are correct... in the environment in which they are correct.

If I have an object that is rotating at a steady rate along a perfectly flat surface with no air friction, you are correct that there must be no force of friction. If there were, it would be an unopposed force, and the object would slow down. Because the object is not slipping, if it slows down, it has to rotate slower, which is in violation of the initial assumptions we made.

On the other hand, consider an object which is accelerating in a no-slip manner, like a ball starting to roll down a ramp. In this situation, the acceleration is increasing the required rotational speed to achieve the no-slip constraint. This means we must have a torque on the object, meaning we must have a force which does not go through the center of mass of the object. The only valid one is friction, so you are correct: there will be a friction force opposing the direction of motion because that creates the torque needed to increase the rotational rate.

The difference in the situations is the accelerations and/or other forces besides friction that are in the picture.

As for a third hand, I'd recommend a very enjoyable Smarter Every Day video about how fast things roll. It's not about exactly the same concept, but it's close. And I am always happy when a trained scientist gets confused about the things that confuse me!

I've been told that during pure rotation friction acts opposite to velocity of center of mass (accompanied by change of normal) and slows it down.

This is incorrect. Static friction is independent of rolling direction!

Three situations to consider:

1. Rolling on a flat surface (no net force). Imagine rolling a billard ball over hard, horizontal ground. As you already know, we are only interested in looking at the contact point. This is where sliding can happen so this is where static friction can appear to try to prevent such sliding.

Now, when rolling horizontally, there are the normal force, the weight and... that's it. Static friction is a force that only appears if there is some risk of sliding it has to prevent - but since there are no forces trying to cause the contact point to slide (the weight and normal force balance out), then there is no purpose for static friction. There is nothing for static friction to hold back against. So static friction is zero (non-existing).

1. Rolling upwards. Imagine a marble rolling in a rough glass bowl. On its way up, gravity pulls down and tries to make the contact point slide. So static friction appears in order to hold the contact point fixed. It of course pulls upwards to balance gravity out.

2. Rolling downwards. The marble continues upwards slower and slower, comes to a brief stop and starts rolling downwards faster and faster. Looking at the contact point, gravity still pulls down and still tries to make the contact point slide. So in order to keep it fixed, static friction appears and pulls upwards to balance gravity out!

The fact that the rolling direction is downwards makes no difference. Static friction appears to prevent sliding, and sliding only depends on the forces that are present. Not on the motion or direction.

And now for some sentences of your to be a bit sharper with...

The point of contact doesn't slip therefore no friction is required

Be careful in this sentence. If it slipped, then kinetic friction would take over, yes. But before it slips static friction can is present. Even if something doesn't slip yet, static friction can still ne there, as we saw in the examples above.

Things don't go on forever; Friction must be present to slow it down.

Also be careful here.

Firstly, things do go on forever. A drifting spaceship or orbiting satellite, do go on forever. Nothing stops them.

Secondly, other forces than friction can slow things down. For example air drag slowing down a skydiver. And in the case of a wheel, the compression and flexing of a soft rubber wheel and displacement of a soft surface (think of driving the bike on a sandy beach) are all factors that absorb energy. This energy is taken from the kinetic motion energy, and thus slows down the rolling without friction being the main cause.

All such factors are combined into a parameter called rolling friction. It is called a "friction" because it gives the same result as other frictions, slowing down the motion, but in reality it is not a friction but just a term for sources of energy loss.

1. Pure wheel rotation in outer space: will rotate forever.

2. Pure rotation in outer space plus CM linear velocity: will rotate forever and CM will move forever.

3. Same as (1) on a frictionless table: rotate forever.

4. Same as (2) on a frictionless table: Rotate forever and move forever.

5. Behavior on a table with friction depends on initial conditions and friction coefficients. For example, drop a rotating wheel on the table, friction will accelerate the CM and de-accelerate rotation. But push a non-rotating wheel on the table, friction will de-accelerate CM and accelerate rotation.

After researching a bit and reading the other answers, I thought it would be best if I compile everything into one answer.

Rolling friction is the opposition to rolling caused by non-ideal scenarios like wind, softness of ball, deformities, brakes(in car). Static friction is the friction which opposes the tendency of relative motion.

Instead of a ball consider a more real life car moving on a straight track.
Case 1: The engine is turned off.
Here non-ideal cases (like not a perfect roll and soft surface) slow down the car and it eventually stops. As the linear acceleration ($a$) decreases, static friction acts opposite to the motion of the car to decrease the frequency of rotation of the wheels and maintain the equation $a=\alpha r$. Static friction always tries to attain pure roll and it ends up slowing the car down.
If you consider no rolling friction then, the car is already doing pure roll and no static friction will act. And hence the car will go on forever.

Case 2: The car is accelerating.
Here the engine is increasing the frequency of the rotation of the wheels. So the point of contact has a tendency to slide instead of roll (as the linear acceleration of the car is not enough to satisfy $a=\alpha r$). So static friction acts in the direction of motion of the car so that the linear acceleration increases and the equation is maintained. So static friction here gives acceleration to the car. But Rolling friction still acts to oppose the motion as the non ideal dissipative forces already mentioned.

Case 3: The car is decelerating.
Here the frequency of rotation of the wheels is slowed down by the brakes. Static friction wants the linear acceleration to also come down to maintain pure roll. So it acts opposite to the motion of the car. Rolling friction here is still opposing the rotation of the wheel.