Kinematics says how motion changes. Dynamics asks why.

Newton's central idea is not that "force causes motion." Objects do not need a force to keep moving. Net force causes acceleration — a change in velocity.

First law: inertia

If the net external force on an object is zero:

then its velocity is constant.

Constant velocity includes the special case of rest.

The first law therefore rejects an everyday intuition produced largely by friction: moving objects do not naturally "run out of motion."

Second law: interaction changes momentum

For constant mass, the familiar form is:

The more general statement is:

where:

Force is therefore a rate of momentum change.

Third law: forces come in interaction pairs

If object A exerts a force on object B, then B exerts an equal-magnitude, opposite-direction force on A.

These forces do not cancel each other on a free-body diagram because they act on different objects.

A book resting on a table illustrates two different pairs:

• Earth pulls the book downward; the book pulls Earth upward.
• The table pushes the book upward; the book pushes the table downward.

The upward normal force and downward weight on the book are not a third-law pair. They happen to balance in this situation because the book's acceleration is zero.

Free-body diagrams

A free-body diagram contains only forces acting on the chosen object or system.

Common forces include:

• weight mg
• normal force
• tension
• friction
• spring force
• drag
• electric or magnetic forces in broader physics

Then apply Newton's second law separately by component:

Friction is not always μ mg

The usual models are:

for kinetic friction, and:

for static friction.

Static friction adjusts up to a maximum. It is not automatically equal to μsN.

Also, N=mg only in particular geometries. On a slope, in an accelerating elevator, or during curved motion, the normal force may differ substantially from weight.

Circular motion

An object moving in a circle of radius r at speed v has inward acceleration:

Therefore the inward net force must satisfy:

"Centripetal force" names this required inward net force; it is not an additional physical interaction.

For a satellite, gravity supplies it. For a car turning on a level road, static friction often supplies it. For a mass on a string, tension may supply it.

Gravitation

For point masses or spherically symmetric bodies:

Near Earth's surface this becomes approximately:

because r changes little compared with Earth's radius.

Physics C bridge

The deeper Newtonian statement is:

For a constant-mass particle this reduces to ma⃗. Calculus becomes essential when force varies with position, velocity or time.

Big idea: Forces describe interactions. The vector sum of the external interactions on a system determines how its momentum changes.

Quantitative anchor

A 70 kg person standing still on level ground has weight of about:

That is roughly 154 pounds-force, though newtons and pounds-force are different units.