Class 11 Physics, Part 1 (NCERT)

Sprint 1

Seven Units That Measure Everything

Learn the seven SI base units, the radian and the steradian, and why every measurement needs a unit.

Sprint 2

Converting Units Without Mistakes

Convert any unit, including squared, cubed and compound units, by treating units like algebra.

Sprint 3

Significant Figures: Which Digits Can You Trust?

Count the significant figures in any measurement, including the tricky zeros, and see why changing units never changes the count.

Sprint 4

Measuring Tiny Things Precisely

Compare instruments by least count, find true sizes from magnified ones, and see why many readings beat a few.

Sprint 5

Scientific Notation And Order Of Magnitude

Write any value as a × 10ᵇ, find its order of magnitude, and estimate sizes from atoms to planets.

Sprint 6

Calculating With Significant Figures

Use significant figures for multiplying and dividing and decimal places for adding and subtracting, so no answer claims more precision than its data.

Sprint 7

Rounding Off The Right Way

Round correctly, including the case where the dropped digit is exactly 5, and keep one extra digit until the last step.

Sprint 8

How Errors Travel Through Calculations

Turn ± errors into percentage errors, combine them for a product, and quote a result with its honest uncertainty.

Sprint 9

Dimensions: What Every Quantity Is Made Of

Write the dimensional formula of a quantity from its defining equation, and use dimensions to convert units between systems.

Sprint 10

Catch Wrong Equations With Dimensions

Test any equation term by term: failing the test proves it wrong, but passing does not prove it right.

Sprint 11

Build Formulas Using Dimensions

Derive a formula from the quantities it depends on by matching powers, and know exactly what this method cannot tell you.

Sprint 12

Review: Units And Measurement

Check what you can now do, revise every rule on one set of cards, and solve mixed problems on units, significant figures and dimensions.

Sprint 13

Point Objects, Position And Displacement

Decide when a moving body can be treated as a point, choose an origin and a positive direction, and tell displacement from path length.

Sprint 14

Average Velocity Vs Average Speed

Work out average velocity from displacement and average speed from path length, and see why the two can differ.

Sprint 15

Reading Position–Time Graphs

Read when motion starts, where things are, who is faster and when one overtakes another from x–t graphs, and plot one from a story.

Sprint 16

Instantaneous Velocity: Speed At One Moment

See velocity at an instant as the limit of average velocity, read it as the slope of a tangent, and calculate it with dx/dt.

Sprint 17

Acceleration: How Fast Velocity Changes

Define average and instantaneous acceleration, read it from graphs, and tell the sign of acceleration apart from speeding up or slowing down.

Sprint 18

Velocity–Time Graphs And The Area Trick

Read motion from velocity–time graphs, and find displacement as the area under them, with its sign.

Sprint 19

Graph Detective: Possible Or Impossible?

Rule out impossible motion graphs, and read the signs of position, velocity and acceleration straight off any graph.

Sprint 20

Where The Equations Of Motion Come From

Derive the three equations of motion from the velocity–time graph and by integration, and know they hold only for constant acceleration.

Sprint 21

Solving Problems With The Equations Of Motion

Solve braking and stopping-distance problems with the right signs, and see why stopping distance grows with the square of speed.

Sprint 22

Free Fall: Letting Things Drop

Use the equations with a = −g for objects dropped from rest, prove Galileo's law of odd numbers, and measure your own reaction time.

Sprint 23

Throwing Up: Rise, Stop And Fall

Solve upward-throw problems in one step with signed positions, and draw the speed–time graph of a bouncing ball.

Sprint 24

Relative Velocity: Motion Seen From Another Car

Work out the velocity of one moving body as seen from another moving along the same line.

Sprint 25

Review: Motion In A Straight Line

Check what you can now do, revise every equation and sign rule, and solve mixed motion problems and graph questions on your own.

Sprint 26

Scalars And Vectors: Does Direction Matter?

Tell scalars from vectors, and see what really makes a quantity a scalar.

Sprint 27

Position, Displacement And Equal Vectors

Draw position and displacement vectors, see why displacement ignores the path, and decide when two vectors are equal.

Sprint 28

Scaling And Adding Vectors By Drawing

Multiply a vector by a number, and add vectors head to tail or by the parallelogram method.

Sprint 29

Subtracting Vectors And The Zero Vector

Subtract vectors by adding the opposite, meet the null vector, and prove the four vector inequalities.

Sprint 30

Splitting A Vector Into Components

Write any vector as components along two directions, use unit vectors, and move between components and magnitude-and-angle.

Sprint 31

Adding Vectors By Their Components

Add and subtract any number of vectors by adding their x-, y- and z-components, then find the resultant's size and direction.

Sprint 32

Law Of Cosines And The Racing Boat

Find the size and direction of the resultant of two vectors at any angle, and tell a resultant velocity from a relative one.

Sprint 33

Velocity And Acceleration In A Plane

Find velocity and acceleration as vectors from a position vector, and see why velocity always points along the path.

Sprint 34

Constant Acceleration In Two Directions

Treat motion in a plane with constant acceleration as two separate straight-line motions linked only by time.

Sprint 35

Projectile Motion: Two Motions In One

Split a projectile's motion into a steady sideways motion and a free fall, and show that its path is a parabola.

Sprint 36

Height, Flight Time And Range

Derive and use the projectile formulas for time to the top, time of flight, maximum height and range, and see why 45° goes farthest.

Sprint 37

Uniform Circular Motion: Always Turning In

See why motion in a circle at steady speed is accelerated, find the centripetal acceleration, and use angular speed, period and frequency.

Sprint 38

Review: Motion In A Plane

Check what you can now do, revise every vector, projectile and circular-motion formula, and solve mixed problems on your own.

Sprint 39

Aristotle's Mistake And Galileo's Inertia

See why it looks as if motion needs a force, what friction was hiding, and how Galileo's inclined planes revealed inertia.

Sprint 40

Newton's First Law: No Net Force, No Acceleration

Use the first law in both directions: from forces to motion, and from observed motion back to the forces.

Sprint 41

Momentum And The Second Law: F = Ma

Define momentum, state the second law, meet the newton, and solve force problems by joining F = ma to the equations of motion.

Sprint 42

The Second Law Is A Vector, Local Law

Apply F = ma along each axis, to whole systems, and moment by moment: force now decides acceleration now.

Sprint 43

Impulse: Big Force, Short Time

Measure a brief, large force by its effect: impulse equals the change in momentum.

Sprint 44

Third Law: Forces Always Come In Pairs

Find the partner of every force, see why action and reaction never cancel on one body, and use the law to find forces on a wall.

Sprint 45

Conservation Of Momentum: Recoil And Collisions

Derive momentum conservation from the second and third laws and use it for recoil, collisions and explosions.

Sprint 46

Equilibrium: When All Forces Balance

Balance two, three or many forces on a particle, as a closed polygon or component by component.

Sprint 47

The Everyday Forces Of Mechanics

Gravity, normal reaction, friction, buoyancy, drag, spring force and tension: where each comes from and how to name it.

Sprint 48

Friction: Static, Kinetic And Rolling

Use the laws of static and kinetic friction, find the angle of repose, and see where friction is a nuisance and where we need it.

Sprint 49

Centripetal Force: Turning On A Level Road

Find the real force behind every circular motion, and the top speed for a turn on a level road.

Sprint 50

Banked Roads: Turning Without Skidding

Tilt the road so the normal force helps turn the car, and find the optimum and maximum speeds.

Sprint 51

Free-Body Diagrams: The Problem-Solving Method

Choose a system, draw every force on it, and solve. Then use the method on a sinking floor and a lift.

Sprint 52

Connected Bodies: Strings, Pulleys And Trolleys

Solve two bodies tied by a string: one free-body diagram each, one equation each, the same acceleration.

Sprint 53

Review: Laws Of Motion

Check what you can now do, revise every law and formula, and solve mixed force problems on your own.

Sprint 54

The Dot Product: Multiplying Two Vectors

Multiply two vectors to get a number: A·B = AB cos θ. Use it for angles and projections.

Sprint 55

The Work-Energy Theorem

See where work and kinetic energy come from, and use the theorem to find the work of a force you can't even describe.

Sprint 56

Work: Force Along The Displacement

Work counts only the part of a force along the motion: find its size and sign, and spot the three ways to do no work at all.

Sprint 57

Kinetic Energy: Energy Of Motion

Use K = ½mv², compare kinetic energies across a huge range, and see why 10% of the energy is not 10% of the speed.

Sprint 58

Work By A Variable Force: Area Under The Graph

When the force changes along the way, the work is the area under the F–x graph, or the integral of F dx.

Sprint 59

Potential Energy: Energy Stored By Position

Store energy by working against gravity or a spring, link force and potential by F = −dV/dx, and see why only some forces have one.

Sprint 60

Conservation Of Mechanical Energy

With only conservative forces at work, K + V stays fixed. Use it for falling balls, swings and a bob looping a vertical circle.

Sprint 61

Spring Energy And Potential Energy Graphs

Store energy in a spring as ½kx², use it for a crash-test bumper, and read where a particle can and can't go from a V(x) graph.

Sprint 62

When Friction Steals Energy

With friction, mechanical energy changes by the work friction does: E_f − Eᵢ = W_nc. Redo the crash test with a rough road.

Sprint 63

Power: How Fast Work Is Done

Measure how fast work is done: P = dW/dt = F·v. Use watts, horsepower, kilowatt-hours and efficiency.

Sprint 64

Real-World Energy: Wind, Sun And Exercise

Estimate real energy flows: the power in wind, the area of solar panels for a home, and the fat burned lifting weights.

Sprint 65

Collisions: Elastic, Inelastic, Sticking Together

Momentum is conserved in every collision, kinetic energy only in elastic ones. Find the energy lost when bodies stick.

Sprint 66

Elastic Collisions In One Dimension

Solve a head-on elastic collision with momentum and energy together, and see why light nuclei slow neutrons best.

Sprint 67

Collisions In Two Dimensions

Conserve momentum along x and y separately, count the unknowns, and show that equal masses fly apart at right angles.

Sprint 68

Review: Work, Energy And Power

Check what you can now do, revise every energy formula, and solve mixed problems on your own.

Sprint 69

How Rigid Bodies Move: Slide, Spin, Roll

Tell pure translation, rotation about a fixed axis and rolling apart, and meet the spinning top's precession.

Sprint 70

Centre Of Mass: The System's Balance Point

Find the centre of mass of a few particles as a mass-weighted average position, in one, two or three dimensions.

Sprint 71

Centre Of Mass Of Rods, Plates And Cut-Outs

Use integrals, symmetry, splitting into parts and the cut-out trick to find the centre of mass of real shapes.

Sprint 72

Motion Of The Centre Of Mass And Total Momentum

The centre of mass moves as if all the mass were there and only external forces acted on it, whatever happens inside.

Sprint 73

The Cross Product: A Vector From Two Vectors

Multiply two vectors to get a vector: size ab sin θ, direction by the right-hand rule, and a determinant for components.

Sprint 74

Angular Velocity And Angular Acceleration

Every point of a rotating body shares one ω, but moves at v = ωr⊥. Write it as v = ω × r.

Sprint 75

Torque: The Turning Effect Of A Force

Measure a force's turning effect as τ = r × F: its size from the lever arm, its direction by the right-hand rule.

Sprint 76

Angular Momentum And Its Conservation

Define l = r × p, link it to torque by dl/dt = τ, and see when a system's angular momentum stays constant.

Sprint 77

Equilibrium, Couples And Levers

A rigid body balances only when both the net force and the net torque are zero. Meet the couple and the lever.

Sprint 78

Centre Of Gravity And Balancing Problems

Find where gravity's torque acts, then solve bars on knife edges, a ladder against a wall and a car on its wheels.

Sprint 79

Moment Of Inertia: Resistance To Turning

Find the rotational analogue of mass, I = Σmr², use the standard values, and the radius of gyration.

Sprint 80

Rotational Kinematics: Equations Of Turning

Use the rotational versions of the equations of motion: θ, ω and α in place of x, v and a.

Sprint 81

Rotational Dynamics: Τ = Iα, Work And Power

Torque does work τ dθ, delivers power τω and gives angular acceleration α = τ/I, the rotational F = ma.

Sprint 82

Spinning Faster: Conservation Of Angular Momentum

With no external torque, Iω stays constant: pull the mass in and you spin faster, and your muscles supply the extra energy.

Sprint 83

Review: Systems Of Particles And Rotational Motion

Check what you can now do, revise every rotation formula, and solve mixed problems on your own.

Sprint 84

Kepler's Three Laws Of Planetary Motion

Ellipses with the Sun at a focus, equal areas in equal times, and T² ∝ a³, checked against real planet data.

Sprint 85

Newton's Universal Law Of Gravitation

From the falling apple to the Moon: F = Gm₁m₂/r², its vector form, adding forces from several masses, and where two pulls cancel.

Sprint 86

Spherical Shells And Measuring G

How a hollow shell pulls points outside and inside it, why gravity cannot be shielded, and how Cavendish measured G.

Sprint 87

Acceleration Due To Gravity: Up, Down And At The Surface

g = GM_E/R_E², how g falls as you go up and as you go down, and how g lets us weigh the Earth.

Sprint 88

Gravitational Potential Energy And Potential

From mgh to −GMm/r: why gravitational potential energy is negative, what potential means, and the energy of a group of masses.

Sprint 89

Escape Speed: Leaving Earth For Good

The launch speed that never falls back, v_e = √(2gR_E) ≈ 11.2 km/s, and energy problems with one or two attracting bodies.

Sprint 90

Earth Satellites: Orbital Speed And Period

Gravity as the centripetal force: orbital speed and period, Kepler's third law for satellites, and weighing Mars, the Earth and the Sun from their orbits.

Sprint 91

Satellite Energy, Weightlessness And Tides

Why a satellite's total energy is negative, what it costs to raise or free one, why astronauts float, and why the Moon rules the tides.

Sprint 92

Review: Gravitation

Check what you can now do, revise every gravitation formula, and solve mixed problems on your own.