📂Classical Mechanics

Newton's Laws of Motion

Newton’s Laws of Motion ¹

English mathematician and physicist Isaac Newton presented three laws about motion in 1687 in Principia as follows:

1. An object not subjected to an external force does not change its state of motion.

2. The change in motion is proportional to the applied force on the object.

3. When object 1 applies a force to object 2, object 2 simultaneously applies a force equal in magnitude and opposite in direction on object 1.

These three laws are collectively called Newton’s laws of motion, and are individually referred to as the 1st, 2nd, and 3rd laws, respectively. Furthermore, the branch of science that describes the motion of objects based on these laws is called Newtonian mechanics or classical mechanics.

First Law

Commonly known as the law of inertia. Inertia is a property inherent to all objects that describes their resistance to changes in their motion. In other words, a stationary object does not attempt to move, and a moving object does not attempt to stop. This property is inertia. A stationary object requires an external force to move, and conversely, a moving object requires an external force to stop. The space where this law applies well is called an inertia frame of reference. By this definition, it’s understood that accelerating frames are not inertial frames. For example, when viewing a stationary (seated) object in an accelerating car from another frame of reference, the object appears to be accelerating, meaning its state of motion is changing without an external force.

Second Law

The second law is mainly

$$ \mathbf{F}=m\mathbf{a} $$

expressed by this formula. However, a more detailed expression is as follows.

$$ \mathbf{F}=\frac{ d \mathbf{p}}{ d t} $$

Newton defined the physical quantity that represents the motion of an object as momentum. He also defined force as something that changes the state of motion of an object. Therefore, a change in the state of motion of an object means that its momentum is changing. This leads to the formula that the force $\mathbf{F}$ applied to an object is proportional to the rate of change of momentum, which is exactly what the above formula signifies.

Third Law

Commonly called the law of action and reaction. Among the two forces described in the law, one is referred to as action, and the other, reaction.