# Frictional forces and their directions

Recently I asked a question regarding frictional forces at math stack-exchange(because its basically part of maths syllabus) and I drew some conclusions.

1. If A and B are in rough contact and are in limiting equilibrium, then there exist two frictional forces. One acting on A and one acting on B.

2. The direction of frictional forces can be determined by working out the direction of motion if the friction was not present.(This is a trick to work out the direction of frictional force which was mentioned on https://physics.stackexchange.com/a/94837/128083)

3. The direction of friction forces on A and B are opposite.

1,2 are trivial and were implied on the math stack exchange link. However, I came up with rule 3 by observing the relative velocities of each object.

Let's say A is a wall and B is a ball that is in rough contact with A. From A perspective, B is falling down hence an upward friction force should be acting on B. From B's perspective, A is moving upwards, hence a downward force should act on A.

However the problem arises in the following question (By downward and upward, I mean upward tangential and downward tangential at point P)

The ball P is moving downwards. An upwards frictional force acts on P. Edit An upward frictional force at P imply a downward frictional force for the disc at P. Since frictional force is opposite the direction of movement, thus a downward friction imply an upward movement and hence a clockwise moment. However, it seems trivial that the disc should rotate anti-clockwise but using the rule 3, we can conclude that motion is clockwise.

Can somebody please explain the fallacies in the proposed rule 3? If there does exist a fallacy please explain some alternative that I can employ in working out the direction of frictional forces.

The link mentioned above is: https://math.stackexchange.com/q/2303592/335742

Since frictional force is opposite the direction of movement...

Frictional forces are opposite the direction of relative movement. It is not the case that it is opposite absolute movement.

Imagine dropping an object onto a conveyor belt moving to the right. Friction from the belt onto the object causes it to move to the right also. So friction and motion are not opposite.

But until it reaches the same speed, the object is moving to the left compared to the belt.

Going back to your disc, if there were zero friction, the disc would not rotate. The ball would simply slide down. In such a case the relative motion between the objects would be the ball moving down compared to the disc. That tells you that the friction between the two would be "up" on the ball and "down" on the disk. That direction of friction is a force and gives you the acceleration. The ball falls more slowly than it would in zero friction, and the disc accelerates counterclockwise.

• Can you please clear how did you knew that by the downward movement of the ball the direction of friction on the disc is downwards? May 31, 2017 at 18:47
• Without friction, the ball would be pulled down by gravity and would move down relative to the disc (because there are no other tangential forces on the disc, it would remain at rest). Friction acts opposite to this relative motion (up on the ball, down on the disc). May 31, 2017 at 18:50
• Okay so I assume you're using the analogy I gave in my question when explaining rule 3. So the reason the disc rotates is because there is an unbalanced force (frictional) and hence it rotates in the direction of the force. Right? I have understood the rest of your answer. Just one thing what you meant by " But until it reaches the same speed, the object is moving to the left compared to the belt." When same speed, the relative motion is 0. How can this a relative velocity arise in left direction (from belt perspective). May 31, 2017 at 18:58
• The situation started with relative motion because the belt was moving and the object was placed on it. The belt is moving right (relative to the room). The object is not moving (relative to the room). So the object is moving left relative to the belt. As friction accelerates the object to the right, the relative speed between belt and object decreases to zero. May 31, 2017 at 19:02

Assume there is relative motion between the two bodies with one body moving faster than the other one.

The frictional force on the slower body is such as to try to increase its speed so as to reduce the relative motion between the bodies.
The frictional force on the faster body is such to try to decrease its speed so as to reduce the relative motion between the bodies.

So you have the two frictional forces acting in opposite directions both trying to reduce the relative motion between the bodies.

A similar argument can be put forward for two bodies which are moving in opposite directions
In this case the frictional force on one body acts in the same direction as the direction of motion of the other body and the same is true of the other body.
The net result is the frictional forces trying to reduce the relative motion between the two bodies.

In both cases the frictional forces acting on the two bodies are in opposite directions and equal in magnitude - Newton's third law.

• For the example you posed for the Newton's third law, it is necessary for their "speeds" to be same if I want the friction forces equal. Right? May 31, 2017 at 21:16
• @FaiqRaees It is always true so you could have one object not moving and the other object moving and it would be kinetic friction. May 31, 2017 at 21:18
• Oh so frictional forces no matter what will be same because the relative speed for the objects will always be same. Thank you. May 31, 2017 at 21:19

You have the mentioned the answer yourself! Since an upward frictional force acts on P, a downward frictional force acts on the disc, at the point of contact of P, and hence it rotates anti-clockwise (Notice, the direction of frictional forces is in opposite direction, not the direction of movement) (Though, to be exact, the frictional forces aren't in the directly upward or downward direction. They are in the direction of the tangent at P)

• Please see edit. May 31, 2017 at 17:31
• I think friction forces and direction of movement for a respective body, are in opposite directions. Thus a downward friction, imply a clockwise movement for the disc( which will be cancelled out by the friction present). May 31, 2017 at 17:33
• You are confusing the relative motion (or possible motion) of the two objects with the overall motion of the objects. Imagine a moving train and you slide an object towards the back of the train. The friction from object to the floor acts towards the back of the train but the train is still moving forward, isn't it?
– nasu
May 31, 2017 at 18:32