🚀 Classical Mechanics

📘 Mechanics Study Guide

The complete mechanics study guide: kinematics, Newton's laws, friction, energy, momentum, and rotation — with formulas, checklists, and exam tactics.

Acceleration — Definition, Formula and Worked Examples

Acceleration is the rate of change of velocity: a = Δv/Δt. Units, vector direction, sign conventions, and worked examples from cars to free fall.

Center of Mass — The Balance Point That Moves Simply

The balance point of any object or system: how to locate the center of mass, why it moves as if all mass were there, and what that predicts.

Circular Motion and Centripetal Force Explained

Why circular motion needs a center-seeking force: a = v²/r and F = mv²/r, with examples from roundabouts to satellites.

Elastic Collisions in Detail — Conserving Momentum and Kinetic Energy

Collisions where kinetic energy is conserved: the defining conditions, the 1D equations, the equal-mass velocity swap, and worked examples.

Friction Force — Static vs Kinetic Friction Explained

Friction opposes sliding: static vs kinetic friction, the formula f = μN, the role of the normal force, and worked examples.

Newton's Law of Universal Gravitation — The Inverse-Square Force

Newton's law of universal gravitation: the inverse-square force between masses, the value of G, and why weight equals mg.

Inelastic Collisions in Detail — Lost Energy, Kept Momentum

Collisions where kinetic energy is not conserved: momentum still rules, perfectly inelastic sticking, energy-loss calculation, and explosions in reverse.

Kepler's Laws of Planetary Motion — Ellipses, Areas and Periods

Kepler's three laws of planetary motion — elliptical orbits, equal areas in equal times, and the T² ∝ a³ harmony — and how Newton explained them.

Conservation of Momentum — Collisions Explained

Momentum p = mv is conserved in collisions. Impulse, elastic vs inelastic collisions, and worked examples from car crashes to rockets.

Newton's First Law of Motion — Inertia Explained

Newton's first law: objects keep doing what they're doing unless a net force acts. Inertia, balanced forces, and why things stop on Earth.

Newton's Second Law — F = ma Explained with Examples

F = ma: how net force, mass and acceleration connect. Units, direction, net vs applied force, and worked examples from cars to rockets.

Newton's Third Law — Action and Reaction, Clearly Explained

For every action there is an equal and opposite reaction. What action-reaction pairs really are, why they don't cancel, and classic examples.

Projectile Motion Explained — Trajectories, Range and Height

Why thrown objects follow a curved path, the independence of horizontal and vertical motion, range and height formulas, and worked examples.

Simple Pendulum Motion — Period, Restoring Force and Timekeeping

How a swinging mass on a string keeps time: the restoring force, the period formula T = 2π√(L/g), and why mass and amplitude don't matter.

Static Equilibrium — Zero Net Force and Zero Net Torque

The two conditions for staying at rest — zero net force and zero net torque — with torque explained, seesaw and ladder examples, and stability.

The SUVAT Equations — Constant-Acceleration Kinematics

The five SUVAT equations for motion with constant acceleration: what s, u, v, a and t mean, how to choose the right equation, and fully worked examples.

Torque Explained — The Physics of Turning Things

Torque is τ = rF sin θ: why a longer wrench loosens bolts easier, how direction is found with the right-hand rule, and the rotational form of Newton's…

Work-Energy Theorem — Work Equals Change in Kinetic Energy

W = Fd and the work-energy theorem: net work equals change in kinetic energy. Derivation sketch, units, and worked examples.

Angular Momentum Explained — L = Iω and Its Conservation

What angular momentum is, why L = Iω is conserved without external torque, and how skaters, divers and satellites exploit it.

Rotational Kinematics — Angular Displacement, Velocity and Acceleration

Angular displacement, velocity and acceleration: the rotational analogs of SUVAT, the radian, and how rotation connects to linear motion.

L = Iω — Angular Momentum

Angular momentum equals moment of inertia times angular velocity.

Centripetal Force — F = mv²/r

The inward force needed for circular motion equals mass times speed squared divided by radius.

F = Gm₁m₂/r² — Newton's Law of Universal Gravitation

Gravitational force equals G times the product of the masses divided by the distance squared.

Gravitational Potential Energy — PE = mgh

Gravitational potential energy equals mass times gravity times height.

Hooke's Law — F = kx

The restoring force of a spring equals its stiffness times the displacement from equilibrium.

Kinetic Energy Formula — KE = ½mv²

Kinetic energy equals one-half times mass times velocity squared.

Momentum Formula — p = mv

Momentum equals mass times velocity.

Newton's Second Law — F = ma

The net force on an object equals its mass times its acceleration.

v = √(GM/r) — Circular Orbital Velocity

Orbital speed equals the square root of G times central mass over orbital radius.

T = 2π√(L/g) — Period of a Simple Pendulum

Period equals two pi times the square root of length over g.

Power Formula — P = W/t

Power equals work done divided by the time taken.

PE = ½kx² — Elastic Potential Energy of a Spring

Spring potential energy equals one-half times the spring constant times the stretch squared.

s = ut + ½at² — Displacement under Constant Acceleration

Displacement equals initial velocity times time plus one-half acceleration times time squared.

v = u + at — Velocity from Acceleration and Time

Final velocity equals initial velocity plus acceleration times time.

τ = rF·sinθ — Torque (Moment of Force)

Torque equals lever arm times force times the sine of the angle between them.

Work Formula — W = Fd

Work equals force times distance moved in the direction of the force.

🧮 Acceleration Calculator

🧮 Angular Velocity Calculator — ω = Δθ/Δt

🧮 Centripetal Acceleration Calculator — a = v²/r

🧮 Escape Velocity Calculator — v = √(2GM/r)

🧮 Free Fall Calculator

🧮 Friction Force Calculator

🧮 Gravitational Force Calculator — F = Gm₁m₂/r²

🧮 Impulse Calculator — J = FΔt

🧮 Kinetic Energy Calculator

🧮 Momentum Calculator

🧮 Newton's Second Law Calculator (F = ma)

🧮 Orbital Velocity Calculator — v = √(GM/r)

🧮 Potential Energy Calculator

🧮 Power Calculator

🧮 Projectile Range Calculator

🧮 Speed and Velocity Calculator

🧮 Hooke's Law Calculator — F = kx

🧮 Elastic Potential Energy Calculator — PE = ½kx²

🧮 SUVAT Calculator — s = (u + v)t / 2

🧮 SUVAT Displacement Calculator — s = ut + ½at²

🧮 SUVAT Calculator — v² = u² + 2as

🧮 SUVAT Velocity Calculator — v = u + at

🧮 Torque Calculator — τ = rF sin θ

Circular Motion Simulator

Spin a mass on a string: change the radius, speed and mass to discover exactly how centripetal force depends on each one.

Collision Lab Simulator

Crash two carts head-on: set their masses and velocities, flip between elastic and sticky collisions, and verify momentum conservation.

Free Fall Simulator

Drop objects from any height in a vacuum. Measure fall time and impact speed — and see why mass does not matter.

Inclined Plane Simulator

Slide a block down a ramp: tilt the angle, dial friction up and down, and watch the acceleration respond in real time.

Pendulum Simulator

Swing a pendulum with any length, mass and angle. Verify that the period depends on length — not mass.

Projectile Motion Simulator

Launch projectiles at any speed and angle. Watch the trajectory live and discover why 45° gives maximum range.

Spring-Mass Oscillator Simulator

Stretch a spring-mass system with any stiffness and mass. Watch simple harmonic motion and test the period formula.

Circular Motion Practice

10 problems · 10 practice problems on circular motion — centripetal force, acceleration, orbital speed and banked …

Energy and Momentum Practice — Work, Power and Collisions

10 problems · 10 practice problems on work, energy, power and momentum — conservation laws, collisions and real ca…

Forces Practice — Newton's Laws Problems

10 problems · 10 practice problems on forces and Newton's laws — net force, inertia, friction and action-reaction …

Friction Practice Set 2

10 problems · 10 practice problems on friction — static vs kinetic, friction on inclines, and friction in accelera…

Gravitation Practice

10 problems · 10 practice problems on gravitation — Newton's law, orbital motion, escape velocity and weightlessne…

Kinematics Practice — Motion, Speed and Acceleration Problems

10 problems · 10 practice problems on kinematics — speed, velocity, acceleration and SUVAT equations — with instan…

Momentum and Collisions Practice 2

10 problems · 10 practice problems on momentum and collisions — elastic vs inelastic, impulse, and recoil.…

Projectile Motion Practice

10 problems · 10 practice problems on projectile motion — range, height, flight time and the independence of horiz…

SUVAT Equations Practice

10 problems · 10 practice problems on the SUVAT equations of uniformly accelerated motion — choosing the right equ…

Torque Practice

10 problems · 10 practice problems on torque — lever arms, balance, rotational equilibrium and the vector nature o…

Work and Energy Practice 2

10 problems · 10 practice problems applying the work-energy theorem — work by gravity, springs, brakes and power.…