Mechanics

(the branch of physics studying motion and the forces that cause it)

What is mechanics?

Mechanics is the branch of physics that studies motion and the forces that cause it. It rests on three laws, first stated by Isaac Newton in 1687, that describe how objects move and interact.

Newton's three laws

First law (inertia): an object at rest stays at rest, and an object in motion keeps moving at a constant speed in a straight line, unless a force acts on it. A ball rolling on a perfectly frictionless floor would never slow down on its own — it only stops because friction, a real force, acts on it.

Second law: force equals mass times acceleration, written F = ma. A heavier object needs more force to speed it up by the same amount as a lighter one — this is exactly why pushing an empty shopping cart is easier than pushing a full one with the same effort.

Third law: for every action, there is an equal and opposite reaction. When you push against a wall, the wall pushes back on you with exactly the same amount of force, in the opposite direction.

A real proof: momentum is conserved when two objects collide

Momentum is defined as mass times velocity (p = mv). Here is a genuine proof, not just an observation, that when two objects collide, their total momentum before the collision equals their total momentum after.

During the collision, object A pushes on object B with some force, and by Newton's third law, object B pushes back on object A with the exact same force, in the opposite direction, for the exact same amount of time. Force multiplied by time equals the change in momentum (this follows directly from F = ma, since acceleration is the rate of change of velocity over time). Since the two forces are equal and opposite, and act for the same duration, the change in momentum of object A is exactly equal and opposite to the change in momentum of object B. So whatever momentum A loses, B gains, and whatever A gains, B loses — meaning the total combined momentum of the two objects never changes during the collision.

A worked example

A 2 kg ball moving at 3 m/s (momentum = 6 kg·m/s) collides with a stationary 1 kg ball. If the moving ball ends up traveling at 1 m/s afterward, its momentum is now 2 kg·m/s — a loss of 4 kg·m/s. By the proof above, the second ball must have gained exactly that 4 kg·m/s of momentum: since its mass is 1 kg, its final velocity must be 4 m/s. This can be checked directly by measurement, and it always holds, for any collision.

Why mechanics matters

Every moving object — a car, a thrown ball, a planet orbiting the sun — obeys these same three laws. Mechanics is the foundation that lets engineers design safe vehicles, that lets astronomers predict where a planet will be years in advance, and that underlies nearly every other branch of physics.