# How a wheel move on the earth?

I was wondering how a wheel move on the earth ,I mean if friction causes it moves so what causes it stops after a while without any pushing force? I think that the direction of the friction force is depended on the velocity of the lowest point of the wheel which is in touch with earth. please pay attention to the picture I uploaded. if it is not right,please tell me the answer.

## 1 Answer

Imagine that the wheel is stationary. A force is applied which accelerates the wheel horizontally. This add translational momentum to the wheel. Now, since the wheel does not slide, a frictional force is produced at point P which produces a torque on the wheel. The torque causes the wheel to start rolling, adding rotational momentum. Once the wheel is moving at a constant rate, there is no frictional force at point P. The wheel will continue to move and rotate at the same rate under it's own inertia. No frictional force is required to keep the wheel rolling. Even with a frictional force between the wheel and the road, an ideal wheel will continue to roll forever. If there where no friction force, the wheel would slide instead of roll. The reason that wheels in the real world slow down after a while is because they are constructed from real materials. The weight of the wheel causes the contact point P to deform slightly, and possibly deform the ground, too. There is energy lost doing this deformation, which is why the wheel will eventually slow down and stop.

An extreme example of deformation in a wheel is a flat tire on a bike. It is much harder to roll a flat tire than one that is inflated. That is because deforming the shape of the tire as it touches the ground uses up a lot of energy. All real wheels will deform due to their weight, although sometimes it is too small to see.

• would you please answer me how the rotational momentum and and linear momentum turns to each other?can you explain it more?what are the relations between them? – Abbas Shojakani Feb 12 '16 at 17:59
• It depends on the shape of the wheel. Linear momentum is m*v where v is the speed along the ground. Rotational momentum is Iω where ω is the angular velocity. Angular velocity is related to the linear velocity by ω=v/r where r is the radius of the wheel. The exact relation depends on the shape of the wheel because of the angular moment of inertia, I. Different shaped wheels have different moment of inertia so the exact proportion of linear to angular momentum can vary. – user235504 Feb 12 '16 at 19:44
• can you write an example?please – Abbas Shojakani Feb 17 '16 at 5:03