Mechanics

Mechanics is the branch of physics that deals with the motion of objects and the forces that cause this motion. It is one of the oldest and most fundamental branches of physics, dating back to the work of Galileo Galilei and Isaac Newton.

Mechanics can be divided into several sub-branches:

• Classical mechanics: Deals with the motion of macroscopic objects at speeds much less than the speed of light
• Relativistic mechanics: Extends classical mechanics to objects moving at speeds comparable to the speed of light
• Quantum mechanics: Deals with the behavior of particles at the atomic and subatomic level

In pre-university physics, we primarily focus on classical mechanics.

Newton's laws of motion form the foundation of classical mechanics. There are three laws:

First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction, unless acted upon by an unbalanced force.

This law introduces the concept of inertia, which is the resistance of an object to changes in its state of motion. The more mass an object has, the greater its inertia.

Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Mathematically, this is expressed as:

F = ma

Where:

• F is the net force acting on the object (in newtons, N)
• m is the mass of the object (in kilograms, kg)
• a is the acceleration of the object (in meters per second squared, m/s²)

Third Law: For every action, there is an equal and opposite reaction.

This means that when one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

A force is a push or pull that can cause an object to accelerate. Forces are vector quantities, meaning they have both magnitude and direction.

Common types of forces include:

• Gravitational force: The attraction between objects with mass
• Normal force: The perpendicular force exerted by a surface on an object
• Friction: The force that opposes the relative motion of surfaces in contact
• Tension: The force transmitted through a string, rope, or cable
• Spring force: The force exerted by a compressed or stretched spring

The net force on an object is the vector sum of all individual forces acting on it.

Work is done when a force causes an object to move. Mathematically, work is the dot product of force and displacement:

W = F·d·cos(θ)

Where:

• W is the work done (in joules, J)
• F is the force applied (in newtons, N)
• d is the displacement (in meters, m)
• θ is the angle between the force and displacement vectors

Energy is the capacity to do work. There are many forms of energy, including:

• Kinetic energy: Energy of motion, given by E_k = ½mv²
• Potential energy: Energy due to position or configuration
• Gravitational potential energy: E_p = mgh (near Earth's surface)
• Elastic potential energy: Energy stored in a stretched or compressed spring, given by E_e = ½kx²

The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another.

Power is the rate at which work is done or energy is transferred. It is given by:

P = W/t or P = F·v

Where:

• P is power (in watts, W)
• W is work (in joules, J)
• t is time (in seconds, s)
• F is force (in newtons, N)
• v is velocity (in meters per second, m/s)

Momentum is the product of an object's mass and velocity. It is a vector quantity:

p = mv

Where:

• p is momentum (in kg·m/s)
• m is mass (in kg)
• v is velocity (in m/s)

The law of conservation of momentum states that in a closed system, the total momentum remains constant if no external forces act on the system.

Impulse is the change in momentum and is equal to the product of force and the time interval over which the force acts:

J = F·Δt = Δp

Where:

• J is impulse (in N·s)
• F is force (in N)
• Δt is the time interval (in s)
• Δp is the change in momentum (in kg·m/s)

This relationship is known as the impulse-momentum theorem.