Newton's Laws
of Motion

The three fundamental laws defining the relationship between an object's motion and the forces acting upon it.

Objects at Rest or in Motion

Newton's First Law states that an object will remain at rest, or continue to move in a straight line at a constant velocity, unless acted upon by a net external force.

$$\sum \vec{F} = 0 \iff \frac{d\vec{v}}{dt} = 0$$
Real World Analogy

The Sudden Stop

When a car brakes abruptly, you lurch forward. Your body is attempting to maintain its constant forward velocity because no net horizontal force was immediately applied directly to you.

Force and Acceleration

Newton's Second Law describes how the velocity of an object changes when it is subjected to an external force. The acceleration of an object is directly proportional to the net force applied, and inversely proportional to its mass.

$$\vec{F} = m\vec{a}$$
Relationship

Mass as Resistance

More massive objects require greater force to achieve the same acceleration.

Equal and Opposite

For every action, there is an equal and opposite reaction. When two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction.

$$\vec{F}_{AB} = -\vec{F}_{BA}$$
Misconception

Forces don't always result in equal movement

Even though the forces are strictly equal, the accelerations of the two objects may be vastly different if their masses differ, as required by the Second Law $(a = F/m)$.

Academic References