Newton's Laws of Motion

Newton's first law — a body remains at rest, or continues to move at constant velocity, unless acted on by a resultant force.

The first law defines what a force does: it changes velocity. It also disposes of the intuition that motion needs a continuous force to sustain it. A puck sliding on ice travels far not because something pushes it, but because almost nothing opposes it.

Newton's second law — the rate of change of momentum of a body is proportional to the resultant force, and takes place in the direction of that force.

F = ma

for constant mass, since F = Δp/Δt = mΔv/Δt = ma. The momentum form is more general and is the one that handles changing mass.

Newton's third law — if body A exerts a force on body B, then body B exerts an equal and opposite force on body A.

What makes a genuine third law pair — the two forces must act on different bodies, be of the same type, be equal in magnitude and opposite in direction. All four conditions must hold.

Example: a book rests on a table. Its weight and the normal contact force are equal and opposite, but they are not a third law pair — both act on the book, and they are different types of force. They balance because the book is in equilibrium, which is the first law, not the third. The partner of the book's weight is the book's gravitational pull on the Earth; the partner of the normal contact force is the book pushing down on the table.

Why third law pairs never cancel — they act on different bodies, so they can never appear together on the same free-body diagram. Forces only cancel when they act on the same object.

Example: this resolves the old puzzle about a horse pulling a cart. The cart pulls back on the horse just as hard, but that force acts on the horse, not on the cart. What accelerates the cart is the forward pull from the horse minus friction on the cart — a calculation about the cart alone.