# Tangential Contact forces between objects

My book says that there are two forces two objects experience when they're in contact with each other. (it uses an example of a cylinder and a parallelepiped that are in contact with eachother) The chapter is about statics.

1) The normal force.

2) A tangential force, tangential to both surfaces that are in contact with each other. This happens only when the surfaces are rough.

I find this strange because I have never seen the second. The book further states that to be in static equilibrium, these tangential forces can't exceed the maximum force of static friction. I would understand this if the tangential force comes from an external source but I have never seen that two surfaces experience tangential forces due to their contact alone. Can someone clarify this?

## 2 Answers

Yes, you are correct. Let's take the simplest example of a block resting on a rough table. In this case, only the normal force exists. Now, apply a very small force (which doesn't exceed static friction) to one side of the block. The block won't slide because the static friction exactly opposes your applied force. This is not the maximum static friction force because the threshold has not been exceeded yet. This is the tangential force that you mentioned. It arises because the surfaces attempt to slide with respect to each other (because of some other force), but the tangential force that is static friction is exactly what is preventing this from happening.

Summary: The tangential force is the static friction preventing the surfaces from sliding with respect to each other.

• Thanks, It's weird that my book says that the tangential forces are due to contact alone. – delivosa Oct 3 '18 at 12:35
• @delivosa: Yes, the surfaces must be trying to slide, and if you use $F < \mu_s N$, the normal force can't be zero as well (i.e. they must be pressing against each other). – Vincent Thacker Oct 3 '18 at 12:36
• +1. A small comment: To "The tangential force arises due to static friction" I would rather say that the tangential force is the static friction. – Steeven Oct 3 '18 at 13:43
• @Steeven: You have a point; that makes much more sense. – Vincent Thacker Oct 3 '18 at 13:56

The tangential force acts tangentially to the surface of objects when two objects are in contact with each other. This tangential force balances forces associated with their masses. However, this force acts only when the surfaces of both objects are rough enough. In order for the system to be in equilibrium, this force must exist.