Net Force

Also called Resultant force, Sum of forces

The net force on a system is the vector sum of all the forces exerted on it. Zero net force does not mean no forces: a book resting on a table has two forces on it and a net force of zero.

The net force is the one force that would have the same effect as all the real forces together. Because forces are vectors, you add them by components, not by magnitude.

F⃗net=∑iF⃗i\vec{F}_{\text{net}} = \sum_i \vec{F}_i

What the equation sheet actually gives you. Not that sum. The AP Physics 1 sheet prints the second law solved for acceleration:

a⃗sys=∑F⃗msys=F⃗netmsys\vec{a}_{\text{sys}} = \frac{\sum \vec{F}}{m_{\text{sys}}} = \frac{\vec{F}_{\text{net}}}{m_{\text{sys}}}

The equilibrium condition ∑iF⃗i=0\sum_i \vec{F}_i = 0 is a derived equation rather than a printed one. You get it by setting the acceleration to zero, which forces the numerator to zero, and you are expected to produce that in one step.

Zero net force is not no force. It is a balance. Newton's first law says a system with zero net force keeps a constant velocity, which includes staying at rest but is not limited to it.

Direction survives the addition. Acceleration points along the net force, always. If the net force is perpendicular to the velocity, the speed does not change but the direction does, which is how circular motion works.

Finding the net force from a diagram is a routine: see how to find net force, and check numbers with the net force calculator.

Back to the physics glossary