Branches of Mechanics

Mechanics is divided into three major branches, each focusing on a different aspect of motion.

Kinematics

Kinematics describes motion without considering the forces that cause it.

It answers questions like:

• How far has an object traveled?
• How fast is it moving?
• How does its velocity change with time?

Key quantities in kinematics include:

• Position ($\vec{r}$)
• Velocity ($\vec{v}$)
• Acceleration ($\vec{a}$)

Dynamics

Dynamics studies the relationship between motion and its causes, namely forces.

It answers questions such as:

• What force is required to produce a certain motion?
• How does mass affect acceleration?

Dynamics is governed by Newton’s laws of motion, which form the backbone of classical mechanics.

Statics

Statics deals with systems in equilibrium, where there is no net motion.

The condition for equilibrium is:

$$ \sum \vec{F} = 0 $$

This means that all forces acting on the object balance each other.

Applications include:

• Structural engineering
• Stability of buildings and bridges
• Mechanical equilibrium in machines