Class 9 Exam Preparation
Class 9 Physics Formula Sheet
Revise the essential formulas for motion, force, gravity, work, energy, simple machines and sound from one interactive study page.
How to Use This Formula Sheet
Read the condition written below each formula before substituting numerical values. Keep all quantities in compatible SI units and follow one sign convention throughout a calculation.
Identify the quantity
Write what is given and what must be calculated before selecting an equation.
Convert the units
Convert kilometres, hours, centimetres or grams when the required formula uses metres, seconds or kilograms.
Check the answer
Write the unit with the final value and consider whether the result is physically reasonable.
Important Symbols
A symbol can represent different quantities in different chapters. Always read the definition given with the question.
Motion
Distance, displacement, speed, velocity and acceleration
Average Speed
Use total path length, including every part of the journey.
SI unit: m/sAverage Velocity
Displacement is the directed change from the initial position to the final position.
SI unit: m/sAcceleration
Acceleration is the rate at which velocity changes with time. A negative value can represent acceleration opposite to the chosen positive direction.
SI unit: m/s2First Equation of Motion
Use for motion in a straight line with constant acceleration.
Relates velocity and timeSecond Equation of Motion
Use for displacement during straight-line motion with constant acceleration.
Displacement in metresThird Equation of Motion
This equation is useful when time is not provided.
Constant acceleration onlyDisplacement from Average Velocity
Under constant acceleration, average velocity is (u + v) divided by 2.
Constant acceleration onlyUniform Circular Speed
Here, r is the radius and T is the time taken for one complete revolution.
SI unit: m/sPosition-Time Graph
The slope of a position-time graph gives velocity.
Slope unit: m/sVelocity-Time Graph
Area below graph = displacement
Treat areas below the time axis as negative when using a signed velocity graph.
Graph interpretationSpeed Conversion
1 m/s = 18/5 km/h
Multiply by 5/18 to change km/h into m/s. Multiply by 18/5 for the reverse conversion.
Unit conversionForce and Laws of Motion
Net force, momentum and Newton's laws
Newton's Second Law
F is the net force. The acceleration is in the direction of the net force.
SI unit of force: newton, NAcceleration Produced by Force
For the same net force, a larger mass has a smaller acceleration.
Acceleration: m/s2Linear Momentum
Momentum has the same direction as velocity.
SI unit: kg m/sRate of Change of Momentum
This is the momentum form of Newton's second law. For constant mass, it becomes F = ma.
Net forceForces in the Same Direction
Add the magnitudes when both forces act along the same direction.
Resultant forceForces in Opposite Directions
The resultant acts in the direction of the larger force.
Resultant forceAction-Reaction Pair
The forces are equal in magnitude and opposite in direction, but they act on two different objects.
Newton's third lawBalanced Forces
The object remains at rest or continues with constant velocity.
Newton's first lawGravitation and Weight
Gravitational attraction, free fall, mass and weight
Universal Law of Gravitation
r is the distance between the centres of the two masses.
G approximately 6.67 × 10−11 N m2/kg2Acceleration Due to Gravity
M is the mass of the planet and R is the distance from its centre. At the surface, R is the planet's radius.
Near Earth's surface: about 9.8 m/s2Weight of an Object
Weight is the gravitational force acting on an object. Mass is measured in kilograms, while weight is measured in newtons.
SI unit of weight: NMass from Weight
Use this equation when weight and the local value of g are known.
SI unit of mass: kgVelocity During Free Fall
This form treats the direction of gravitational acceleration as positive. Change the sign of g when the chosen positive direction is upward.
Uniform g near Earth's surfaceFree-Fall Displacement
Replace a with g in the second kinematic equation and use the selected sign convention.
Displacement in metresFree Fall Without Time
Use this equation when the time of motion is not given.
Use signs consistentlyObject Dropped from Rest
v = gt
s = 1/2 gt2
These forms apply when the initial velocity is zero and downward is selected as positive.
Free-fall special caseWork, Energy and Simple Machines
Work done, energy conversion, power and mechanical advantage
Positive Work
Use this form when force and displacement are in the same direction.
1 joule = 1 newton metreNegative Work
Work is negative when force acts opposite to displacement, as in many situations involving friction.
SI unit: JZero Work
Work is zero when there is no displacement or when force is perpendicular to displacement.
No energy transfer by that forceKinetic Energy
Kinetic energy depends on mass and on the square of velocity.
SI unit: JGravitational Potential Energy
h is the vertical height measured from the selected reference level.
SI unit: JWork-Energy Theorem
The net work done on an object equals the change in its kinetic energy.
Work and energy in joulesMechanical Energy
In an ideal system where no other external force removes energy, the total mechanical energy remains constant.
SI unit: JPower
Power measures how quickly work is done or energy is transferred.
1 watt = 1 joule per secondMechanical Advantage
Mechanical advantage compares the load moved with the applied effort.
No unitIdeal Fixed Pulley
A fixed pulley changes the direction of effort but does not reduce its ideal magnitude.
Ideal conditionIdeal Inclined Plane
L is the length of the inclined plane and h is its vertical height. Friction is ignored in this ideal relation.
No unitPrinciple of a Lever
= Load × load arm
The arms are perpendicular distances measured from the fulcrum to the corresponding lines of action.
Balanced leverMechanical Advantage of a Lever
Increasing the effort arm can reduce the effort required for the same load.
Ideal leverSound
Oscillations, frequency, time period, wavelength and echoes
Frequency
N is the number of complete oscillations made in time t.
SI unit: hertz, HzTime Period
Time period is the time required for one complete oscillation.
SI unit: second, sFrequency-Time Period Relation
T = 1 / f
Frequency and time period are reciprocals of one another.
Hz and sWave-Speed Relation
v is wave speed, f is frequency and λ is wavelength.
m/s = Hz multiplied by mWavelength
Use compatible units so that wavelength is obtained in metres.
SI unit: mFrequency from Wave Speed
Frequency remains fixed by the vibrating source when a wave moves from one medium into another.
SI unit: HzDistance Using an Echo
The measured time includes the journey to the reflecting surface and the return journey, so the total distance is divided by 2.
Distance in metresDistance Travelled by Sound
This is the ordinary distance-speed-time relation for uniform wave speed in a medium.
Distance in metresNumber of Oscillations
Multiply frequency by elapsed time to find the number of complete oscillations.
N has no unitEssential SI Units
Write the correct symbol and respect capitalisation. For example, newton is written as N, joule as J and watt as W.
| Quantity | SI Unit | Unit Symbol |
|---|---|---|
| Distance and displacement | metre | m |
| Speed and velocity | metre per second | m/s |
| Acceleration | metre per second squared | m/s2 |
| Mass | kilogram | kg |
| Force and weight | newton | N |
| Momentum | kilogram metre per second | kg m/s |
| Work and energy | joule | J |
| Power | watt | W |
| Frequency | hertz | Hz |
| Wavelength | metre | m |
Before substitution
Write the known quantities with their units and convert them into a consistent unit system.
During calculation
Substitute values only after writing the formula. Keep sufficient digits until the final step.
For vector quantities
Use direction words, signs or arrows for displacement, velocity, acceleration, force and momentum.
In the final answer
Include the numerical value, correct SI unit and direction when the direction is required.
Interactive Physics Calculator
Select a formula, enter values in the displayed units and calculate the result instantly.
Calculation Practice
The calculator provides the numerical result, but you should still show the formula, substitution and unit in an examination.
Quick Formula Quiz
Choose one answer for each question and then check your score.
1. What is 72 km/h in m/s?
Answer: 72 multiplied by 5/18 equals 20 m/s.
2. What net force gives a 5 kg object an acceleration of 2 m/s2?
Answer: F = ma = 5 multiplied by 2 = 10 N.
3. Find the kinetic energy of a 2 kg object moving at 3 m/s.
Answer: K = 1/2 multiplied by 2 multiplied by 3 squared = 9 J.
4. A wave travels at 340 m/s and has a frequency of 170 Hz. What is its wavelength?
Answer: Wavelength = 340 divided by 170 = 2 m.
5. A machine lifts a load of 300 N using an effort of 100 N. What is its mechanical advantage?
Answer: MA = load divided by effort = 300 divided by 100 = 3.
Frequently Asked Questions
Review these common questions before practising Class 9 physics numericals.
The major formula areas include motion, force and momentum, gravity and weight, work and energy, mechanical advantage, wave speed, frequency, time period, wavelength and echo distance.
They are used for motion in a straight line when acceleration is constant. The selected positive and negative directions must be used consistently.
Mass describes the amount of matter and is measured in kilograms. Weight is the gravitational force on that mass, equals mg and is measured in newtons.
Mechanical advantage equals load divided by effort. For an ideal inclined plane it equals length divided by vertical height, and for an ideal lever it equals effort arm divided by load arm.
Important relations include f = 1/T, v = f lambda and echo distance = vt/2 when t is the total time taken by the sound to travel to the reflecting surface and return.
Convert the provided quantities into compatible units before substitution. Write the correct unit with the final answer and include direction when required.