5.6 : Newton's Second Law

Newton's second law is closely related to his first law of motion. It mathematically gives the cause-and-effect relationship between force and changes in motion. Newton's second law is quantitative and is used extensively to calculate what happens in situations involving a force. All external forces acting on a system add together to produce a net force F_net. A larger net external force produces a larger acceleration. This acceleration is directly proportional to, and in the same direction as, the net external force acting on a system.

Further, it also seems reasonable that acceleration should be inversely proportional to the mass of a system. In other words, the larger the mass (the inertia), the smaller the acceleration produced by a given force. Experiments have shown that acceleration is exactly inversely proportional to mass, just as it is directly proportional to net external force. It has been found that the acceleration of an object depends only on the net external force and the mass of the object. Combining the two proportionalities yields Newton's second law, which states: The acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and is inversely proportional to its mass.

The second law describes how a body responds mechanically to its environment. The influence of the environment is the net force, the body's response is the acceleration, and the strength of the response is inversely proportional to the mass.

Newton also outlined his second law in terms of momentum: The instantaneous rate at which a body's momentum changes is equal to the net force acting on the body.

This text is adapted from Openstax, University Physics Volume 1, Section 5.3: Newton's Second Law.