One of the core ideas from your mechanics course is that objects accelerate in response to forces. This page collects the key ideas about forces in one place. If your recollection of any of these concepts isn't clear, you may want to go back and review the details in the readings from Physics 183.

A force is anything that pushes or pulls on an object. Since we push an object in a specific direction, a force has a direction associated with it: force is a vector quantity, $\vec{F}$, with three separate components $F_x$, $F_y$, and $F_z$. If you are adding forces together, you need to add the components separately. If we are only talking about the magnitude of the force, irrespective of its direction, we leave off the little vector arrow and just write $F$ (like we did for the three individual components).

The SI unit of force is the newton (N), which is defined as the force needed to accelerate a mass of 1 kg at a rate of 1 m/s². In other words, 1 N = 1 kg m / s².

Forces are the means by which objects interact with each other. There are two sides to every interaction, which means that every force is part of a pair, sometimes called an interaction pair or an action-reaction pair. In other words, if object A exerts a force on object B, then object B is also exerting a force on object A.

Newton's Third Law tells us that the magnitude of the force experienced by each object is the same – it's a single interaction, and the two forces are just two sides of the same coin. But the directions of the two forces are opposite: if I push you forward, then the rebound force pushes me backward. Mathematically, we represent this as $$\vec{F}_\textrm{A on B} = -\vec{F}_\textrm{B on A}.$$

Although every force has an interaction partner, we don't always care about the partner force. If both of the interacting objects are part of our system, such as two small charged particles exerting electric forces on each other, then we generally need to keep track of both sides of the interaction and we will write down two forces. We sometimes say that these forces are internal to our system.

But if an object in our system interacts with something outside of our system, we usually don't keep track of the reaction force. For example, if I drop a ball, I say that the ball experiences a gravitational force from the Earth. But I usually ignore the gravitational pull that my ball exerts on the Earth (even though it is just as big as the force on my ball!), because I'm thinking of the Earth as part of the external environment rather than part of my system, and I'm not trying to track the Earth's motion. In this case, we say that the Earth's gravitational pull is an external force and not part of an interaction pair.

In your mechanics course you probably studied several types of forces:

• Gravity: near the Earth's surface, every object experiences a force with magnitude $F_g = mg$ pulling downward (toward the center of the Earth). In this equation, $m$ is the object's mass and $g$ = 9.8 m/s² is the gravitational acceleration.
• Spring force/Hooke's Law: an object attached to a spring has an equilibrium position where it experiences zero net force. If the object is moved away from its equilibrium position by a distance $\Delta x$, it experiences a force $F_{sp} = -k \Delta x$ pushing it back toward the equilibrium position. Here $k$ is the spring constant of that particular spring, and the minus sign indicates that the force is in the opposite direction of the object's displacement: if the object is in front of its equilibrium position, the spring forces pulls backward, and vice versa.
• Normal force: if an object rests on a surface, the surface exerts a force on it to prevent it from sinking into the surface. This is called the normal force because the direction of the force is always perpendicular (normal) to the plane of the surface. The surface never actually pushes the object away, so it only exerts as much force as it needs to keep the object from penetrating the surface. This means there's no general formula for the magnitude of the normal force, it can only be calculated based on the other forces acting on the object. The weight of the object is the interaction partner force to the normal force.
• Friction: if two surfaces try to slide across each other, they experience a frictional force.