Rolling and friction

Classical Mechanics Level 1

When the velocity of the center $v$ and the angular velocity $\omega$ of a round object are related as $\vec v = \vec \omega \times \vec r,$ where $\vec r$ is the position vector of the particle with respect to the center of the round object, which friction will act on the rolling object at an instant?

The surface is horizontal and rough.
No other force acts in the horizontal direction.

No friction Kinetic friction Rolling friction Static friction

3 solutions

Silvia Tamburini
Mar 27, 2018

I actually didn’t understand this one. Static friction is acting on the ball at the contact point, and that’s basically why the ball is rolling without slithering. Rolling friction is also acting on the ball, but on short distances it’s negligible compared to static friction. At least, this is what I studied. If I'm wrong, please correct me!

I agree with you

Atin Bainada - 2 years, 4 months ago

Rolling Friction is due to a component of the Normal force, say due to roughness on the surface of the road or indentations of the ground or deformations of the ball that produces a component of non-zero torque. Draw an image of a ball rolling and deforming the ground and convince yourself that the component of the normal force is at a contact point slightly ahead of the center line. Thus, this produces a torque that slows down the ball.

Max Yuen - 2 years ago

I said: it is true that rolling friction acts on a rolling object. But try rolling a ball on a plane: it will stop, eventually, but after a long time. That's because the rolling friction is small. Static friction is more powerful, and it causes the ball to roll. So if the question is 'which force acts on a rolling ball on a plane?', there are two answers: static friction and rolling friction. And probably if you want to choose one of them, it should be static friction.

Silvia Tamburini - 1 year, 10 months ago

Max Yuen
Jun 10, 2019

This one is tricky, since Rolling Friction is the only one that doesn't involve a tangential force. The action can be a normal force due to a deformed ball or deformed ground that produces a lightly offset line or action that results in a torque. If the ground is rough, it will do nothing unless less the roughness involves loose gravel and sand that can be crushed or if energy can be dissipated by moving the gravel and sand. The list goes on. It's not a simple force to consider.

Sebastian Jakov
Apr 25, 2019

Static friction acts on the system if and only if the object isn´t moving yet. Kinetic friction acts when the object moves but I understand that is the name assigned to the friction of objects like cubes or a box while moving on a rough surface, because of the different event that happens when a spheric object is moving (rolling) -that is the deformation of the surface and "tilting" of the Normal force vector- named rolling friction. Then given that the object that is moving is spheric the friction force is called Rolling friction.

Static Friction can act on it even when the ball is rolling. See rolling ball or cylinder down an incline without slipping. Static friction is present, but does zero work. It is just there to convert translational motion to rotational motion.

Max Yuen - 2 years ago

If you consider a ball rolling on a plane, as Max said, static friction acts on the ball; and the reason why this happens is that the point of contact between the ball and the plane is static with respect on the plane. Because of this same reason, static friction does zero work. Rolling friction will eventually act to stop the ball; but, as I said earlier, that will happen in a long time.

Silvia Tamburini - 1 year, 10 months ago

Rolling and friction

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