4.2: Newton's Second Law of Motion

As we saw in Newton's First Law of Motion, an object at rest stays at rest unless acted upon by an external force. Also, an object in motion at constant velocity remains in motion unless acted upon by an external force. Again, this is inertia. The only way to overcome inertia is to accelerate the object. Applying a net force to the system to induce acceleration.

Acceleration is proportional to the net external force on a system. That is, the higher the applied force, the bigger the acceleration. We also know that acceleration is inversely proportional to mass. That is, large objects accelerate at a slower rate than smaller objects. We know this from our everyday observations. It is easier to accelerate a light ball than a heavier bowling ball.

Newton's Second Law of Motion relates net external force to acceleration and mass of the system: $F_{\mathrm{net}} = ma$, where $F_{\mathrm{net}}$ is the net force, $m$ is mass, and $a$ is acceleration. Note that force is a vector quantity, so it has a magnitude and a direction.

The system is whatever we are interested in when calculating a physics problem. The external force is any force that acts upon the system, but is not part of the system. For example, picture pushing a rock up a hill. The system is the rock, and the external force is you pushing the rock.

The unit for force is the Newton, N. The definition of the Newton is $1\ \mathrm{N} = 1\ \mathrm{kg\: m/s^{2}}$.