# Direction of friction on a rolling body

• Happiness
In summary, when a cylinder slows down and comes to a stop on a flat surface without sliding, it is not just friction that is at play, but also the deformation of the surface and cylinder, as well as aerodynamic drag. This leads to a clockwise angular acceleration, contradicting the premise that the cylinder would stop without sliding.
Happiness
A cylinder rolls on a horizontal, flat surface without sliding towards the left, so it must be rolling anticlockwise about its center of mass (CM). Suppose it slows down to a stop due to friction. What is the direction of the friction at the point of contact?

Since it slows down, friction must be acting to the right. But this rightward friction produces an anti-clockwise torque ##\tau## about the CM. Since ##\tau=I\alpha##, this anti-clockwise ##\tau## produces an anti-clockwise angular acceleration ##\alpha## about the CM. Since the cylinder does not slide, a faster rotation means its CM moves faster. This contradicts the premise that the cylinder comes to a stop. What's wrong?

I am guessing any cylinder that comes to a stop must slide. For a cylinder that is not observed to be sliding, it is still sliding but not noticeably. Is this true?

Happiness said:
Since it slows down, friction must be acting to the right. But this rightward friction produces an anti-clockwise torque ##\tau## about the CM. Since ##\tau=I\alpha##, this anti-clockwise ##\tau## produces an anti-clockwise angular acceleration ##\alpha## about the CM. Since the cylinder does not slide, a faster rotation means its CM moves faster. This contradicts the premise that the cylinder comes to a stop. What's wrong?
It's not simple friction that causes the rolling cylinder to slow and stop, but deformation of the surface. (This effect is called "rolling resistance".) The effect of surface deformation ends up with the reaction force of the surface acting ahead of the center of the cylinder, thus creating a clockwise angular acceleration.

Dale and Happiness
Doc Al said:
It's not simple friction that causes the rolling cylinder to slow and stop, but deformation of the surface...
... and deformation of the cylinder, and aerodynamic drag.

## 1. What is the direction of friction on a rolling body?

The direction of friction on a rolling body is opposite to the direction of motion. This means that as the body rolls forward, the direction of friction will be in the opposite direction, trying to slow down the motion of the body.

## 2. Does the direction of friction change as the body rolls?

Yes, the direction of friction on a rolling body can change. As the body rolls, the direction of motion changes, and therefore, the direction of friction also changes. However, it will always be in the opposite direction of the motion.

## 3. How does the direction of friction affect the rolling motion of a body?

The direction of friction plays a crucial role in the rolling motion of a body. It creates a resistance force that opposes the motion, causing the body to slow down or stop. This allows the body to roll smoothly without slipping or skidding.

## 4. Is the direction of friction the same for all rolling bodies?

No, the direction of friction can vary depending on the type of rolling body and the surface it is rolling on. For example, a ball rolling on a flat surface will have a different direction of friction compared to a car tire rolling on a rough road surface.

## 5. How can the direction of friction on a rolling body be calculated?

The direction of friction can be calculated using the laws of physics and the principles of motion. It involves considering the type of surface, the weight and shape of the rolling body, and the direction and speed of its motion. Calculating the direction of friction accurately is important for understanding and predicting the behavior of rolling bodies.

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