Newton's Second Law of Motion

In the previous section, we defined the concepts of force and mass. We now bring these two quantities together to determine how a net force affects the translational motion of an object. Observations of objects in motion lead to a fundamental relationship: the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.

The Mathematical Formulation

This principle is known as Newton's second law of motion. It is often written as an equation relating the vector sum of all forces (the net force, ΣF) to the mass (m) and the acceleration (a).

It is important to remember that this equation is a vector equation. This means it can be broken down into its scalar components along the x, y, and z axes. For a two-dimensional problem in the x-y plane, we analyze the forces using the following component equations:

Units of Force

From the equation ΣF = ma, we can determine the standard SI unit of force. Since mass is measured in kilograms (kg) and acceleration is measured in meters per second squared (m/s²), the unit of force must be kg·m/s². In honor of Sir Isaac Newton, this combination of units is called the newton (N).

Therefore, 1 N is the exact amount of force required to accelerate a 1-kg mass at a rate of 1 m/s².