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I've been introduced to the normal contact force and have been told that it acts in a direction which is perpendicular to the contact surface.

What I'm confused about is how do we define a normal to a contact surface when there are 2 different directions which the reaction forces act along.

Here are 2 cases where there is a wall and a rod in each case, could someone please explain why the normal reaction force acts in the direction which it does.

Normal reaction Force picture

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2 Answers 2

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The normal contact force is the force exerted by the wall on the rod that prevents the rod penetrating the wall. If the rod is free to move around on the wall (i.e. its end is not fixed in place) then the normal force is always perpendicular to (at right angles to) the surface of the wall at the point of contact.

The reason why the normal force is always perpendicular to the surface of the wall is that we (usually) assume that the wall is completely solid and we want to introduce a constraint that prevents the rod from penetrating the wall.

If the normal force were not perpendicular to the wall then the rod could move unopposed along a line that was perpendicular to the direction of the normal force, and this movement would lead to the rod penetrating the wall. However, if the normal force is always perpendicular to the surface of the wall then the contact point of the rod can only move along the surface of the wall and cannot penetrate the wall.

In addition to the normal force, the wall may exert other forces on the rod such as friction.

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What we call the "normal contact force" is really the normal component of the total contact force. If $\theta$ is the acute angle between the contact force F and the wall, then the normal component of the contact force is $$F_n=F\cos{\theta}$$

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