Physics should be learned by starting from basic properties and using them to analyze phenomena. This essay examines the concept of force, the distinction between net and individual forces, and the role of constraint forces in common misconceptions.
What does it mean to study physics? This is not a question about doing physics research, but about learning physics as a student. A typical path begins by learning the basic properties of the physical world that have been discovered through experiment. These properties are often fundamental enough that they are not proved inside the theory itself. In mathematics, they are somewhat similar to axioms. The magnitude of electromagnetic force acting on small particles, or the gravitational constant, can be understood in this way.
After learning these basic properties, we use them to derive new ones. Suppose we want to find the electromagnetic force acting on a circular plate. A circular plate is ultimately an arrangement of many small particles. So, in principle, the force acting on the whole plate can be found by adding up the forces acting on its smaller parts. These derived results usually have a practical purpose. We study a circular plate rather than a randomly shaped plate because the circular case is useful and manageable.
The derivation itself also teaches a method. The mathematical and physical techniques used to find a formula for a circular plate can often be adapted to other shapes or situations. In that sense, learning physics is not only about memorizing formulas. It is about learning how to move from basic properties to new descriptions of the world.
After deriving formulas, students solve examples to learn how concepts apply to real phenomena. But if the explanation of the basic properties is insufficient, it becomes difficult to solve problems correctly. When students later look at solutions, those solutions often explain only the special situation of the problem rather than the general property behind it. If this pattern repeats, students begin to apply basic principles differently depending on problem type. Instead of analyzing a phenomenon from fundamental concepts, they identify the type of problem and learn the corresponding calculation method.
This makes it difficult to analyze unfamiliar phenomena. The problem appears frequently when students learn the concept of force in classical mechanics. This essay focuses on the meaning of force and the misunderstandings that often form around it.
What is force?
Force is a word we use in ordinary language. Different people may associate it with different images: someone lifting an object, people pushing or pulling each other, political power, or physical strength. Among these everyday images, pushing and pulling is closest to the physical concept of force.
In physics, force is usually described as an interaction that can change the motion, direction, or structure of an object. This definition can feel vague. Compared with other physical quantities, the vagueness becomes more obvious. Momentum, for example, is defined mathematically as the product of mass and velocity. Force, by contrast, can sound almost humanistic rather than mathematical.
This is because force is close to a fundamental physical quantity. Like time, distance, and mass, force is something we measure. However, measuring force is more complicated than measuring time or length.
Before discussing measurement, we need to clarify how force is represented and what net force means. Force is usually drawn with arrows. The starting point of the arrow is placed where the force acts, and the direction and magnitude follow vector notation. The unit of force is the newton. One newton is the force required to accelerate a one-kilogram object at one meter per second squared.
Net force means the vector sum of all forces acting on an object. According to Newton's laws, the net force acting on an object can be found by differentiating its momentum with respect to time. But this is not the definition of net force. It is a property relating force and motion. It also does not directly measure each individual force.
Measuring force
Just as clocks measure time and rulers measure distance, scales measure force. A scale uses elastic force. A spring is the simplest example. It is known that the force with which a spring pulls or pushes is proportional to the amount by which it is stretched or compressed from its natural length. Therefore, we can measure force through the deformation of a spring.
Contact forces, which act through direct contact with an object, can often be measured directly with a scale. Non-contact forces, such as magnetic attraction or repulsion, usually require indirect methods. A common method is to infer force from acceleration using Newton's laws. But force obtained this way is always net force. That point matters.
Imagine that a bar magnet and a circular magnet are both pulling on the same piece of iron. To find the force due to each magnet separately, we need a principle of independent action: the force exerted by one magnet alone continues to act in the same way even when other forces are also present, unless the situation itself changes. Using this idea, individual forces must be separated through controlled experiments.
Some forces have known formulas in terms of other physical quantities. Gravity near Earth's surface is a representative example: the gravitational force on an object is the object's mass multiplied by gravitational acceleration. But not every force is given by a simple formula.
A normal force is a good example. When a cup rests on a table, the table exerts an upward force on the cup. This force is called the normal force. Its magnitude depends on the weight of the cup and other forces acting on it. There is no universal formula for the normal force that applies to all situations. Instead, we use the principle of independent action and Newton's laws to determine it.