The term ‘normal force’ might be misleading to some, especially those without a background in mathematics. It may seem to suggest that the force in the question is straightforward, ordinary, or easy to understand. But as they say, there is always more to it than that.
In this context, the term ‘normal’ means an object (such as a line, ray, or vector) that is positioned in such a way that it makes an angle of 90 degrees to a given object. For example, you’ve probably been told to sit up straight i.e. with your back at 90° to the surface of the chair. In other words, your back should be normal to the surface of the chair.
Read more: What is normal force?
The legs of the chair you are sitting on are probably normal to the ground (i.e. they are at 90 degrees to the surface of the Earth).
In short, if an object is normal to something = the object is at 90 degrees to that thing.
Normal, perpendicular, and right-angled
You may be wondering what is the difference between normal, perpendicular, and right-angled.
In physics and mathematics, the three words mean fundamentally the same thing and are often used interchangeably.
The choice usually depends on the context and taste. For instance, in two and three-dimensional geometry, perpendicular is often used.
Perpendicular lines. The cross is made of two wooden boards perpendicular to each other.
Normal is usually used in regard to vectors whilst right-angled is common in elementary 2D and 3D geometry such as polygons.
For example, a right-angled triangle. A square has four right angles.
But why are there so many words that essentially mean the same thing? Don’t know 🤷♂️but math teachers need something to confuse students a bit eh?
In this article, normal and perpendicular will be used interchangeably.
Introducing the normal force
Forces are directional, they make all sorts of angles with the objects on which they act upon. For example, when you are lifting weights at the gym, you are applying an upward force on them. At a supermarket, you are pushing the cart forward, sitting at a chair, you are pressing it down, and so on. In physics, we say forces are vectors. i.e. they have magnitude as well as direction in space.
Traditionally, the term normal is common when discussing vectors, which is why we have the normal force, rather than the perpendicular force or the right-angled force.
When a force acts perpendicular to an object or a surface, then we say the force is acting normal to that object or surface.
For example, when you are standing up straight on a flat floor, you are actually pressing on the floor with your weight (force) which is acting at 90 degrees to the floor (surface).
However, you are (hopefully!) not sinking into the ground. This is because the surface of the floor is also exerting an upward force on you which balances off with the gravitational force. This force also acts at 90 degrees to the surface of the Earth. i.e. it acts vertically upwards.
This is the force you feel at the soles of your feet.
Both of these forces are acting at 90 degrees to the ground and they are both, by definition, normal forces.
But again, there is always a bit more to it than that.
What makes a force, a ‘normal force’?
Plenty of forces in nature act at 90 degrees on an object, yet they are not the normal force. As we have discussed, your weight is one of them, it acts perpendicular to the surface of the ground yet it is not referred to as the normal force.
All normal forces act perpendicular to an object, but not all forces that act perpendicular to an object are normal forces.
Suppose you are not standing on a flat surface, but on an inclined plane – like a wheelchair ramp.
This time, you will have a hard time standing straight up without leaning forward a little because a component of your weight is pushing you backward. The inclined plane influences the direction of your weight relative to the surface. Thus your weight and the upward force from the floor will have slightly different directions and won’t cancel out as before.
To illustrate this, consider a book resting on an inclined plane.
Its weight is the gravitational force with which the Earth pulls on it, so its direction is vertically downwards.
However, because of the inclination, only a component of the book’s weight will press down on the surface of the plane. The surface will match the weight on it with a force that is always perpendicular to the surface. This is the normal force.
Unlike other perpendicular forces, a normal force is always perpendicular to the surface in contact.
Conclusion
The normal force is a contact force. i.e. it comes into play when two bodies are in contact with each other.
When a force is exerted on a surface, the surface exerts a force back that is always perpendicular to the surface. This is the normal force. Its direction is perpendicular to the surface and its magnitude equals the component exerted at right angles to the surface.
