Frictional wheels without slipping (gear system)

In the figure below it is stated that the friction force should always be greater than the tangential force in order to prevent slipping between two frictional wheels. My question is that if we apply Newton's second law to that contact point won't the tangential force resultant point upwards with the direction of the friction since the tangential force is larger and thus the wheels have an opposite rotating direction?

• The wheels do have opposite rotating directions, just like gears in contact. Jan 27, 2022 at 14:12

The concept behind

the friction force should always be greater than the tangential force

is that the maximum friction force should be greater to the force that causes the rotation of the wheel. If you try to apply more torque, then there will be slipping.

This is very similar to the following concept:

If a small force $$F_A$$ is applied, then the friction force will only be equal to that force $$F_A$$ and the box will not move. If $$F_A$$ exceeds the maximum friction force then the box will slide.

Important Sidenote: That sliding motion is what we usually consider as motion, and sometimes get confused in the case of the gear the OP presented. I.e. the rotation again is considered motion. However, in the case of the gears there is no sliding -- i.e. for the contact point of gear A and gear B the relative velocity is zero, or in another way the move in unison.

• Fully understood, but if the friction force was greater than the tangential force exerted by wheel A then won't it just pull this contact point upwards since the resultant force is pointing upwards(ie Friction>Ftangential, Ffriction-Ftangential>0) Jan 27, 2022 at 14:54
• The friction is always resisting relative motion. E.g. think a cup in a car that accelerates. the friction force on the cup is point towards the acceleration of the car, so that the cup does not move relative to the car. So they point is, friction will always be opposite to relative motion, and it will always be as much as possible so that motion is not permitted. So friction cannot be greater than the motion generating force.
– NMech
Jan 27, 2022 at 14:59
• Thanks for your help Jan 27, 2022 at 15:06