Before we can understand why things move, we need a clear way to describe how they move. This is the job of kinematics. It's the language of motion, focusing on the what, where, and when, without yet asking why.

The three key ideas in kinematics are position, velocity, and acceleration.

• Position ($x$): This is simply where an object is. It’s a location, often measured relative to a starting point or origin.
• Velocity ($v$): This tells us how fast an object's position is changing and in what direction. It’s not just speed; direction matters. Driving 60 miles per hour north is a different velocity from 60 miles per hour south.
• Acceleration ($a$): This is the rate at which an object's velocity changes. You feel acceleration when you press the gas pedal in a car or when you slam on the brakes.

Kinematics describes motion, but dynamics explains it. Dynamics is the study of forces and why they cause objects to accelerate. The foundation of dynamics rests on three simple but powerful laws formulated by Isaac Newton.

Newton's First Law: The Law of Inertia An object in motion stays in motion, and an object at rest stays at rest, unless acted upon by an external force. This property of resisting changes in motion is called inertia. If you slide a book across a table, it stops because of the force of friction. In the vacuum of space, with no friction, a thrown object would just keep going forever.

Newton's Second Law: Force, Mass, and Acceleration This is the most famous of the three, and it connects force, mass, and acceleration with a simple equation. It states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

A bigger force produces more acceleration, while a more massive object requires more force to accelerate at the same rate. It’s harder to push a car than a bicycle.

Newton's Third Law: Action and Reaction For every action, there is an equal and opposite reaction. When you push on a wall, the wall pushes back on you with the same force. This is how rockets work. They push hot gas out the back (action), and the gas pushes the rocket forward (reaction).

Force and motion are intimately connected to the concepts of work and energy. In physics, "work" has a very specific meaning. Work is done when a force causes an object to move a certain distance.

If you push a box across the floor, you are doing work. If you push on a wall and it doesn't move, you might get tired, but you haven't done any work in the physics sense.

Work is a way of transferring energy. Energy is the ability to do work. It comes in many forms, but in mechanics, we often focus on two types:

A key idea is the Law of Conservation of Energy: energy cannot be created or destroyed, only transformed from one form to another. When a roller coaster goes down a hill, its potential energy is converted into kinetic energy. When it goes up the next hill, that kinetic energy is converted back into potential energy.

Imagine trying to stop a rolling bowling ball versus a rolling tennis ball, even if they're moving at the same speed. The bowling ball is much harder to stop. This is because it has more momentum.

Momentum ($p$) is a vector quantity, meaning it has both magnitude and direction. It’s calculated as mass times velocity.

Just like energy, momentum is conserved in a closed system. The Law of Conservation of Momentum states that the total momentum before a collision is equal to the total momentum after the collision. This is why when one billiard ball hits another, their combined motion follows predictable paths.

Now let's review these core concepts of mechanics.

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These foundational ideas—from describing motion to understanding the forces, energy, and momentum behind it—form the bedrock of physics. Mastering them opens the door to understanding nearly every physical interaction in the universe.