# Mechanics & Dynamics

Mechanics is the study of how interactions change motion. Specify the forces
on a system and you can, in principle, predict its entire future — where it
goes, how fast, and when.


_Figure 001 — Projectile motion: constant horizontal velocity, gravity bending the path
into a parabola, the velocity vector tangent at every point.
_

_Figure 002 — A pendulum: gravity's restoring torque gives simple harmonic motion for
small swings.
_

Kinematics comes first — position, velocity, and acceleration as the
geometry of motion, before any mention of what causes it. Vectors carry
that geometry into two and three dimensions.


Then **Newton's laws** supply the cause. Force equals mass
times acceleration is a differential equation for the trajectory, and the
art is learning to read the forces off a situation and write it down.


_Figure 003 — The free-body diagram: isolate the object and draw only the forces acting
on it — weight, normal, friction.
_

Solving the equations directly is often hard, so mechanics leans on
_conservation laws_. Energy is the first: work done on a body
changes its kinetic energy, and stored potential energy converts back into
motion.


**Momentum** is the second, and it makes collisions and
many-body problems tractable. Whatever the internal forces, the total
momentum of an isolated system is unchanged.


_Figure 004 — An elastic collision of equal masses: the velocities simply swap, momentum
and energy both conserved.
_

Extend the same ideas to spinning bodies and you get rotational inertia,
torque, and **angular momentum** — the conserved quantity
behind everything from a spinning top to a planet's orbit.


_Figure 005 — A Keplerian orbit: an ellipse with the star at one focus, the radius
sweeping equal areas in equal times.
_

Gravitation ties it together. One inverse-square law explains falling
apples and planetary orbits alike, and Kepler's empirical rules fall out of
Newton's mechanics as a consequence.


From there the same framework reaches static equilibrium, fluids at rest
and in flow, oscillations and travelling waves, and the thermal behaviour of
matter — one language for the mechanical world.


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## Contents

### 1. Foundations

1. [Measurement and Dimensions](/mechanics/foundations/measurement-and-dimensions)
2. [Vector Algebra](/mechanics/foundations/vector-algebra)

### 2. Kinematics

1. [One-Dimensional Motion](/mechanics/kinematics/one-dimensional-motion)
2. [Motion Graphs](/mechanics/kinematics/motion-graphs)
3. [Projectile Motion](/mechanics/kinematics/projectile-motion)
4. [Relative Motion](/mechanics/kinematics/relative-motion)
5. [Circular Motion](/mechanics/kinematics/circular-motion)

### 3. Dynamics

1. [Newton's Laws](/mechanics/dynamics/newtons-laws)
2. [Free-Body Diagrams](/mechanics/dynamics/free-body-diagrams)
3. [Friction and Curved Motion](/mechanics/dynamics/friction-and-curved-motion)
4. [Numerical Dynamics](/mechanics/dynamics/numerical-dynamics)
5. [Center-of-Mass Systems](/mechanics/dynamics/center-of-mass-systems)

### 4. Energy

1. [Work and Kinetic Energy](/mechanics/energy/work-and-kinetic-energy)
2. [Potential Energy](/mechanics/energy/potential-energy)
3. [Multiparticle Work](/mechanics/energy/multiparticle-work)
4. [Mass-Energy and Binding](/mechanics/energy/mass-energy-and-binding)
5. [Photons and Quantization](/mechanics/energy/photons-and-quantization)

### 5. Momentum

1. [Momentum and Collisions](/mechanics/momentum/momentum-and-collisions)
2. [Center-of-Mass Collisions](/mechanics/momentum/center-of-mass-collisions)
3. [Rocket Propulsion](/mechanics/momentum/rocket-propulsion)

### 6. Rotation

1. [Rotational Inertia](/mechanics/rotation/rotational-inertia)
2. [Rotational Dynamics](/mechanics/rotation/rotational-dynamics)
3. [Rolling Motion](/mechanics/rotation/rolling-motion)
4. [Angular Momentum](/mechanics/rotation/angular-momentum)
5. [Rolling Resistance](/mechanics/rotation/rolling-resistance)
6. [Gyroscopic Precession](/mechanics/rotation/gyroscopic-precession)

### 7. Gravitation and Matter

1. [Keplerian Orbits](/mechanics/gravity-and-matter/keplerian-orbits)
2. [Gravitational Fields](/mechanics/gravity-and-matter/gravitational-fields)
3. [Static Equilibrium](/mechanics/gravity-and-matter/static-equilibrium)
4. [Fluid Statics](/mechanics/gravity-and-matter/fluid-statics)
5. [Fluid Flow](/mechanics/gravity-and-matter/fluid-flow)
6. [Orbital Motion](/mechanics/gravity-and-matter/orbital-motion)
7. [Stress and Elasticity](/mechanics/gravity-and-matter/stress-and-elasticity)

### 8. Oscillations and Waves

1. [Damped Oscillators](/mechanics/oscillations-waves/damped-oscillators)
2. [Travelling Waves](/mechanics/oscillations-waves/travelling-waves)
3. [Wave Superposition](/mechanics/oscillations-waves/wave-superposition)
4. [Standing Waves](/mechanics/oscillations-waves/standing-waves)
5. [Sound Waves](/mechanics/oscillations-waves/sound-waves)
6. [Doppler Effect](/mechanics/oscillations-waves/doppler-effect)
7. [Wave Packets](/mechanics/oscillations-waves/wave-packets)
8. [Beats and Coupling](/mechanics/oscillations-waves/beats-and-coupling)
9. [Simple Harmonic Motion](/mechanics/oscillations-waves/simple-harmonic-motion)
10. [Pendulum Motion](/mechanics/oscillations-waves/pendulum-motion)
11. [Driven Oscillators](/mechanics/oscillations-waves/driven-oscillators)
12. [Wave Boundaries](/mechanics/oscillations-waves/wave-boundaries)

### 9. Thermodynamics

1. [Kinetic Theory of Ideal Gases](/mechanics/thermodynamics/kinetic-theory-of-ideal-gases)
2. [First Law of Thermodynamics](/mechanics/thermodynamics/first-law-of-thermodynamics)
3. [Entropy and the Second Law](/mechanics/thermodynamics/entropy-and-the-second-law)
4. [Thermal Processes](/mechanics/thermodynamics/thermal-processes)
5. [Phase Changes](/mechanics/thermodynamics/phase-changes)
6. [Thermal Machines](/mechanics/thermodynamics/thermal-machines)