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Physics / 01

Mechanics

The study of motion and the forces that produce it. Mechanics gives us the foundation for understanding everything from a falling object to the motion of planets.

What is mechanics?

Mechanics is one of the foundations of physics. It describes how objects move, why their motion changes, and how quantities such as force, momentum, and energy are related.

Before studying complicated physical systems, it is useful to understand a few basic ideas: position, displacement, velocity, acceleration, and force.

Motion

An object is in motion when its position changes with respect to a chosen reference point over time.

Position The location of an object relative to a chosen reference point.
Displacement The change in position of an object, including its direction.
Velocity The rate at which displacement changes with time.
Acceleration The rate at which velocity changes with time.

Equations of motion

For motion with constant acceleration, several useful relationships connect displacement, velocity, acceleration, and time.

First equation

v = u + at

Final velocity = initial velocity + acceleration × time.

Second equation

s = ut + ½at²

Displacement for constant acceleration.

Third equation

v² = u² + 2as

Useful when time is not directly involved.

Force

A force is an interaction that can change the motion of an object. Forces can accelerate objects, change their direction, or deform them.

Newton's laws provide a framework for connecting force, mass, and motion.

Newton's second law

F = ma

Net force equals mass multiplied by acceleration.

Newton's laws

First law — Inertia An object remains at rest or in uniform motion unless a net external force acts on it.
Second law The acceleration of an object depends on the net force acting on it and its mass.
Third law Forces occur in interacting pairs: when one object exerts a force on another, the second exerts an equal and opposite force on the first.

Work and energy

Energy describes the capacity of a system to produce change. Work provides one way of transferring energy through a force acting over a displacement.

Work

W = Fs cos θ

For a constant force acting through a displacement.

Kinetic energy

K = ½mv²

Energy associated with an object's motion.

Gravitational potential energy

U = mgh

Near Earth's surface, for a chosen reference level.

Momentum

Momentum describes the quantity of motion carried by an object. It depends on both its mass and velocity.

Momentum

p = mv

Momentum is a vector quantity.

Quick example

Apply the idea

A 2 kg object experiences a net force of 10 N. What is its acceleration?

Using Newton's second law:

F = ma

a = F / m

Answer: The acceleration is 5 m/s².