# In what frame of reference does friction exists?

What is friction?

Wikipedia defines friction as:

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.

But forces are relative, so in what reference does friction exists? We normally assume that when we say that a force acts on a body, we mean that the force acts on the body from the frame of the ground.

But then consider a block on the truck, both have the same acceleration with respect to the ground and further assume that surface of both are rough.

So in what reference does friction exists in this case? From the respect of ground, there is a force acting on the block, from Newton's laws, in the direction of acceleration. Is this friction force? No, that is the force by which the truck is moving, from this reference I can just regard the block to be part of the truck and there is no need to invoke friction force at all.

Now is there friction force from the reference of truck? No again since the block is not moving at all from the reference of the truck, hence there could be no friction.

So is there friction at all or not in the cases?

Now let the block be made of ice and the surface of the truck is wet, then the acceleration of the block will be different from that of the truck, say it is in the direction of acceleration of the truck but with a lower magnitude than that of the truck. Now from the reference of ground, there must be a force against the acceleration, it is friction. But what type of friction is this? Is this static or kinetic friction?

So in what reference is there a need to introduce friction force? And How does one decide the type of friction from reference other than the surfaces between which the friction exists?

• RE: "just regard the block to be part of the truck and there is no need to invoke friction force at all". That method wouldn't explain the cases (for example, the block is made of ice and the bed of the truck is wet) where the block has a different acceleration than the rest of the truck. Commented Jul 17, 2021 at 14:50

... forces are relative ...

No, they are not. The real forces on an object (and that includes friction) are the same in any reference frame. However, if you work in a non-inertial reference frame (such as the reference frame of an accelerating truck) you may have to introduce pseudo forces in order to pretend that objects (like the block) are in equilibrium when they are not.

In the non-inertial reference frame of a truck accelerating with acceleration $$a$$, there is a backwards pseudo force $$-ma$$ on the block. This is opposed by a forwards friction force $$ma$$, so that the block is stationary relative to the truck.

In the inertial reference frame of the ground, there is only one horizontal force acting on the block, the forwards friction force $$ma$$. This accelerates the block forwards with acceleration $$a$$ so that it is stationary relative to the truck.

Note that the friction force is exactly the same in either reference frame.

(I am assuming throughout that $$a <= \mu g$$, so the maximum static friction is not exceeded and the block does not slip on the truck).

• So am I correct to say that to decide the type and direction of friction, one must shift his frame to that of one of the surfaces in contact, then draw the free body diagram of the other body and then draw a force opposite to the direction of force acting horizontal(parallel to both surfaces). If the body is moving in this frame the friction is kinetic, if not it is static? Commented Jul 18, 2021 at 0:27
• @IDKWTD It is always simpler to use an inertial reference frame - that avoids the need for pseudo forces. The direction of friction will always be parallel to the surface between two objects and will oppose relative motion between them. And don’t forget that equal and opposite friction acts on both objects, by Newton’s third law. Commented Jul 18, 2021 at 4:38
• @IDKWTD : One need not "shift his frame to that of one of the surfaces in contact". Pick any inertial frame -- the difference of velocities of the two surfaces in that frame is the same. That is, the relative velocities of the surfaces are intertial frame independent, so give the same friction force independently of the choice of inertial reference frame. (Suppose you are watching a video taken by a camera moving with constant linear motion. The difference in velocities between the two surfaces is the same regardless of what constant linear motion the camera has.) Commented Jul 18, 2021 at 4:47
• @Eric Towers form an inertial frame of reference there will be no relative velocity between the block and truck, so should I conclude that there is no firicton force? Commented Jul 18, 2021 at 8:56
• @IDKWTD : You have explained elsewhere that you static friction is present when lateral forces are small enough that the associated lateral acceleration is unable to induce lateral velocity and kinetic friction is present when the lateral forces/accelerations are large enough to induce lateral velocity. That is static friction is sticky, causing objects to not start moving when forces/accelerations are small, and kinetic friction is what you get when the accelerations/forces are large enough that relative motion occurs. Having stated there is no relative velocity, ... Commented Jul 18, 2021 at 9:14

Consider the situation where the truck is accelerating with respect to the ground, and also let the block be stationary with respect to the truck, as in your situation. Then consider the frame of reference of the truck.

Then since the truck is an accelerating reference frame, the block feels a "fictitious" force (call it $$G$$), pointing backwards off the truck. If the block is stationary with respect to the truck it must therefore be the case that there exists a force $$F$$ counteracting $$G$$. That is friction.

• Is this a typo: the truck is accelerating from the reference of the truck? Commented Jul 17, 2021 at 14:58
• bad english, let me rephrase
– user21299
Commented Jul 17, 2021 at 15:00
• What type of friction is this? Static or kinetic? Commented Jul 17, 2021 at 15:08

When the truck starts to accelerate, the block tends to stay still because of its inertia. So there is a tendency to a relative motion between the deck and the block. Whenever there is a relative motion or a tendency to the relative motion, there is a friction force, if rough surfaces are in contact with each other. That is the force that accelerate the block with the truck. This is with respect to the ground frame.

If you consider from the reference of truck the block stands still. But it has a fictitious force $$ma$$ to the backward direction because it is moving with $$a$$ acceleration with respect to the ground frame. To balance this force there must be a opposite force, and that is the friction.

Thus, no matter what reference frame you are considering, friction force exists if they are rough surfaces.

• Do the surfaces really need to be rough? If the bed is wet and you have ice cube on top, there is still friction, right? Just much smaller (possibly negligible)? Commented Jul 18, 2021 at 16:23
• @AlexisWilke, yes, surfaces need to be rough. Even an ice cube is not perfectly smooth. That is why it has a tiny amount of friction (it is neglegible, but still there is). And the friction exists in liquids too and it is called 'viscosity'. If you can find perfectly smooth surfuces you can even build a perpetual motion machine!
– ACB
Commented Jul 19, 2021 at 3:07