In mechanics, the net force is the sum of all the forces acting on an object. For example, if two forces are acting upon an object in opposite directions, and one force is greater than the other, the forces can be replaced with a single force that is the difference of the greater and smaller force. That force is the net force. When forces act upon an object, they change its acceleration. The net force is the combined effect of all the forces on the object's acceleration, as described by Newton's second law of motion. When the net force is applied at a specific point on an object, the associated torque can be calculated. The sum of the net force and torque is called the resultant force, which causes the object to rotate in the same way as all the forces acting upon it would if they were applied individually. It is possible for all the forces acting upon an object to produce no torque at all. This happens when the net force is applied along the line of action. In some texts, the terms resultant force and net force are used as if they mean the same thing. This is not always true, especially in complex topics like the motion of spinning objects or situations where everything is perfectly balanced, known as static equilibrium. In these cases, it is important to understand that "net force" and "resultant force" can have distinct meanings.
Concept In physics, a force is considered a vector quantity. This means that it not only has a size (or magnitude) but also a direction in which it acts. We typically represent force with the symbol F in boldface, or sometimes, we place an arrow over the symbol to indicate its vector nature, like this: F {\displaystyle \mathbf {F} } . When we need to visually represent a force, we draw a line segment. This segment starts at a point A, where the force is applied, and ends at another point B. This line not only gives us the direction of the force (from A to B) but also its magnitude: the longer the line, the stronger the force. One of the essential concepts in physics is that forces can be added together, which is the basis of vector addition. This concept has been central to physics since the times of Galileo and Newton, forming the cornerstone of Vector calculus, which came into its own in the late 1800s and early 1900s.
The picture to the right shows how to add two forces using the "tip-to-tail" method. This method involves drawing forces a {\displaystyle {\mathbf {\mathbf {a} }}} , and b {\displaystyle {\mathbf {\mathbf {b} }}} from the tip of the first force. The resulting force, or "total" force, F t = a + b {\displaystyle \mathbf {F} _{t}={\mathbf {\mathbf {a} }}+{\mathbf {\mathbf {b} }}} , is then drawn from the start of the first force (the tail) to the end of the second force (the tip). Grasping this concept is fundamental to understanding how forces interact and combine to influence the motion and equilibrium of objects. When forces are applied to an extended body (a body that's not a single point), they can be applied at different points. Such forces are called 'bound vectors'. It's important to remember that to add these forces together, they need to be considered at the same point. The concept of "net force" comes into play when you look at the total effect of all of these forces on the body. However, the net force alone may not necessarily preserve the motion of the body. This is because, besides the net force, the 'torque' or rotational effect associated with these forces also matters. The net force must be applied at the right point, and with the right associated torque, to replicate the effect of the original forces. When the net force and the appropriate torque are applied at a single point, they together constitute what is known as the resultant force. This resultant force-and-torque combination will have the same effect on the body as all the original forces and their associated torques.
Parallelogram rule for the addition of forces A force is known as a bound vector—which means it has a direction and magnitude and a point of application. A convenient way to define a force is by a line segment from a point A to a point B. If we denote the coordinates of these points as A = (Ax, Ay, Az) and B = (Bx, By, Bz), then the force vector applied at A is given by
F = B − A = ( B x − A x , B y − A y , B z − A z ) . {\displaystyle \mathbf {F} =\mathbf {B} -\mathbf {A} =(B_{x}-A_{x},B_{y}-A_{y},B_{z}-A_{z}).}
The length of the vector B − A {\displaystyle \mathbf {\mathbf {B}} -\mathbf {\mathbf {A}} }
defines the magnitude of F {\displaystyle \mathbf {\mathbf {F}} } and is given by
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