Newton’s Laws of Motion

Newton’s laws describe how motion changes when forces act on objects. They are the bridge between Kinematic descriptions and dynamics.

First law: inertia

An object at rest stays at rest, and an object moving at constant velocity continues moving in a straight line unless acted on by a net external force.

Inertia is the tendency of matter to keep its current state of motion. Mass measures inertia.

Second law: net force changes momentum

The general form is

$${\vec{F}}_{net}=\frac{d\vec{p}}{dt}$$

For constant mass, using Momentum $\vec{p}=m\vec{v}$:

$${\vec{F}}_{net}=m\vec{a}$$

This is not “force causes velocity”; force causes acceleration, i.e. change in velocity.

Third law: interaction pairs

If object A exerts a force on object B, object B exerts an equal and opposite force on object A.

$${\vec{F}}_{A\to B}=-{\vec{F}}_{B\to A}$$

The pair acts on different objects, so they do not cancel each other on a single free-body diagram.

Common pitfalls

• Use net force, not just any one force.
• Constant velocity means zero net force, not zero forces.
• Action-reaction forces are same type, simultaneous, and on different bodies.

Force unit: Newton.