Physics Formulas Master Sheet

Complete collection of essential physics formulas for Class 9 & 10 students following Punjab Curriculum & Textbook Board (PCTB) syllabus. This comprehensive guide includes LaTeX equations, detailed explanations, and practical applications.

How to Use This Formula Sheet

This comprehensive physics formula sheet is designed specifically for Class 9 and 10 students following the Punjab Board curriculum. Each formula is presented with its LaTeX representation, verbal description, and practical applications to help you understand not just what the formula is, but how and when to use it in solving numerical problems.

Tip: Create flashcards with these formulas and practice applying them to different types of problems. Understanding the derivation and application of each formula is more important than mere memorization.

1. Motion Formulas

Average Acceleration

Average acceleration is defined as the rate of change of velocity with respect to time. It measures how quickly an object's velocity changes over a specific time interval.

Definition
$$\text{Average acceleration} = \frac{\text{Change in velocity}}{\text{Time taken}}$$
Formula
$$a_{av} = \frac{v_f - v_i}{t}$$

Equations of Motion

These three equations describe the motion of objects with constant acceleration. They are fundamental to solving kinematics problems.

First Equation
$$v_f = v_i + at$$
Second Equation
$$S = v_i t + \frac{1}{2} at^2$$
Third Equation
$$2aS = v_f^2 - v_i^2$$

Speed Conversion Formulas

These conversion factors are essential for solving problems where units need to be consistent. Always convert all measurements to the same unit system before calculations.

m/s to km/h
$$\text{Multiply speed with } 3.6$$
km/h to m/s
$$\text{Multiply speed with } \frac{10}{36}$$

Basic Motion Formulas

Fundamental formulas for speed, distance, and time relationships.

Speed
$$v = \frac{d}{t}$$
Distance
$$S = vt$$

2. Motion Under Gravity

Equations of Motion Under Gravity

For objects moving under gravity, acceleration $a$ is replaced by gravitational acceleration $g$. The sign of $g$ depends on the direction of motion.

First Equation
$$v_f = v_i + gt$$
Second Equation
$$h = v_i t + \frac{1}{2} gt^2$$
Third Equation
$$2gh = v_f^2 - v_i^2$$

Important Notes for Gravity Problems

  • For bodies falling down freely: Value of $g$ is positive ($+9.8\ \text{m/s}^2$) and $v_i = 0$
  • For bodies moving upward: Value of $g$ is negative ($-9.8\ \text{m/s}^2$) and $v_f = 0$ at maximum height
  • Always consider the direction of motion when assigning signs to $g$

3. Force and Motion

Newton's Laws and Related Formulas

These formulas describe the relationship between force, mass, acceleration, and momentum in various physical situations.

Newton's Second Law
$$F = ma$$
Weight Formula
$$w = mg$$
Force-Momentum Relation
$$F = \frac{\Delta P}{T}$$
Centripetal Force
$$F_c = \frac{mv^2}{r}$$
Frictional Force
$$F_s = \mu mg$$
Force-Momentum
$$F = \frac{\Delta p}{\Delta t}$$

4. Momentum and Impulse

Impulse Formulas

Impulse is the product of force and time, and it equals the change in momentum of an object.

Impulse Definition
$$\text{Impulse} = F \times \Delta t$$
Impulse Calculation
$$\text{Impulse} = \frac{\Delta p}{\Delta t} \times \Delta t$$
Impulse Result
$$\text{Impulse} = \Delta p$$
Impulse Meaning
$$\text{Impulse} = \text{Change in momentum}$$

5. Vectors and Equilibrium

Vector Operations and Equilibrium Conditions

These formulas are essential for analyzing forces as vectors and determining when objects are in equilibrium.

Resultant Force
$$F = \sqrt{F_x^2 + F_y^2}$$
Direction Angle
$$\theta = \tan^{-1}\left(\frac{F_y}{F_x}\right)$$
X-Component
$$F_x = F \cos\theta$$
Y-Component
$$F_y = F \sin\theta$$
Torque (Vector)
$$\tau = r \times F$$
Torque (Scalar)
$$\tau = rF \sin\theta$$

Equilibrium Conditions

For an object to be in equilibrium, both the net force and net torque acting on it must be zero.

First Condition
$$\sum F = 0$$

(Translational Equilibrium)

Second Condition
$$\sum \tau = 0$$

(Rotational Equilibrium)

Principle of Moments
$$\text{Clockwise moments} = \text{Anti clockwise moments}$$

6. Work, Energy and Power

Work, Energy and Power Formulas

These formulas describe the relationships between work, energy, power, and efficiency in physical systems.

Weight
$$w = mg$$
Work Done
$$W = FS \cos\theta$$
Kinetic Energy
$$E_k = \frac{1}{2} mv^2$$
Potential Energy
$$E_p = mgh$$
Mass-Energy
$$E = mc^2$$
Power
$$P = \frac{W}{t}$$
Efficiency
$$\text{Efficiency} = \frac{\text{Output}}{\text{Input}}$$
% Efficiency
$$\%\ \text{Efficiency} = \frac{\text{Output}}{\text{Input}} \times 100$$

7. Properties of Matter

Properties of Matter Formulas

These formulas describe the physical properties of matter including density, pressure, and fluid mechanics.

Weight
$$w = mg$$
Density
$$\rho = \frac{m}{V}$$
Pressure
$$P = \frac{F}{A}$$
Spring Constant
$$k = \frac{F}{x}$$
Hydraulic Press
$$\frac{F_1}{A_1} = \frac{F_2}{A_2}$$
Volume
$$V = L \times B \times H$$
Pressure at Depth
$$P = \rho g h$$

8. Waves and Sound

Wave Properties

Formulas describing wave motion, frequency, period, and speed relationships.

Time Period of Simple Pendulum
$$T = 2\pi\sqrt{\frac{l}{g}}$$
Speed of Wave
$$v = f\lambda$$
Time Period
$$T = \frac{1}{f}$$
Frequency
$$f = \frac{n}{t}$$
Speed
$$v = \frac{d}{t}$$
Distance
$$S = vt$$

Sound Intensity

Formulas for sound intensity and decibel level calculations.

Intensity Level of Sound
$$\text{Intensity level} = 10 \log\left(\frac{I}{I_0}\right)$$

9. Geometrical Optics

Mirror and Lens Formulas

Fundamental formulas for mirrors and lenses including mirror formula, magnification, and relationships between focal length and radius of curvature.

Mirror Formula
$$\frac{1}{f} = \frac{1}{p} + \frac{1}{q}$$
Radius-Focal Length Relation
$$f = \frac{R}{2}$$
Magnification Formula
$$M = \frac{h_i}{h_o} = \frac{q}{p}$$
Power of Lens
$$\text{Power} = \frac{1}{\text{focal length in meters}}$$
Diopter Definition
$$1D = 1m^{-1}$$

Refraction and Refractive Index

Formulas related to refraction, Snell's law, and critical angle calculations.

Refractive Index
$$n = \frac{\text{Speed of light in air}}{\text{Speed of light in medium}}$$
Snell's Law (air to glass)
$$n = \frac{\sin i}{\sin r}$$
Snell's Law (glass to air)
$$n = \frac{\sin r}{\sin i}$$
Total Refractive Index
$$n = \frac{n_1}{n_2}$$
Critical Angle
$$\sin c = \frac{1}{n}$$

Sign Conventions

For Mirrors:

  • Always (+ve f) for concave (converging) mirror
  • Always (-ve f) for convex (diverging) mirror
  • Real image always lie in front of mirror (+q)
  • Virtual image always lie behind the mirror (-q)

For Lenses:

  • Always (+ve f) for convex (converging) lens
  • Always (-ve f) for concave (diverging) lens
  • Real image always lie on other side of object (Right side of lens) (+q)
  • Virtual image always lie on same side of object (left side of lens) (-q)

Note: When the image distance is positive, the image is on the same side of the mirror as the object, and it is real and inverted. When the image distance is negative, the image is behind the mirror, so the image is virtual and upright. A negative M means that the image is inverted. Positive M means an upright image.

10. Electrostatics

Electrostatic Formulas

Formulas describing electric charge, Coulomb's law, electric fields, and electric potential.

Quantization Rule
$$Q = ne$$
Energy Supplied by Charge
$$E = q(V_a - V_b)$$
Coulomb's Law
$$F = k\frac{q_1 q_2}{r^2},\quad k=9\times10^9\ \text{Nm}^2\text{C}^{-2}$$
Electric Field Intensity
$$E = \frac{F}{q_0}$$
Electric Potential
$$V = \frac{W}{q}$$
Capacitor Formula
$$Q = CV$$

Capacitor Combinations

Formulas for equivalent capacitance in series and parallel combinations.

Series Combination
$$\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2}$$
Parallel Combination
$$C_{eq} = C_1 + C_2$$

11. Current Electricity

Basic Electrical Formulas

Fundamental formulas for current, resistance, power, and energy in electrical circuits.

Electric Current
$$I = \frac{Q}{t}$$

Current = Charge / Time

Ohm's Law
$$V = IR$$

Voltage = Current × Resistance

Electric Power
$$P = \frac{W}{t} = I^2R = IV$$

Multiple equivalent forms

Electrical Energy
$$W = QV$$

Energy = Charge × Voltage

Joule's Law
$$W = I^2Rt = \frac{V^2t}{R}$$

Heat energy in resistors

Resistor Combinations

Formulas for equivalent resistance in series and parallel circuits.

Series Circuit
$$R_e = R_1 + R_2 + R_3 + \cdots$$

Resistances add directly

Parallel Circuit
$$\frac{1}{R_e} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots$$

Reciprocal of sum of reciprocals

Electrical Energy and Billing

Formulas for calculating electrical energy consumption and electricity bills. These are particularly important for practical applications.

Energy Calculation

Energy in kWh
$$\text{Energy} = \frac{P \times t}{1000}$$

P = Power in Watts

t = Time in hours

Energy in kilowatt-hours

Detailed Form
$$\text{kWh} = \frac{\text{Power(W)} \times \text{Time(h)}}{1000}$$

Cost Calculation

Electricity Price
$$\text{Cost} = \frac{P \times t \times \text{Rate}}{1000}$$

P = Power in Watts

t = Time in hours

Rate = Price per kWh

Monthly Bill
$$\text{Bill} = \frac{P \times t \times \text{Rate} \times 30}{1000}$$

For 30-day monthly calculation

Example Calculation

Scenario: A 100W bulb used for 5 hours daily at Rs. 5 per unit

Daily Energy:
$$\frac{100 \times 5}{1000} = 0.5\ \text{kWh}$$
Daily Cost:
$$0.5 \times 5 = Rs. 2.5$$
Monthly Cost:
$$2.5 \times 30 = Rs. 75$$

12. Electromagnetism

Transformer Formulas

Formulas describing the operation and characteristics of transformers.

Transformer Ratio
$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$
Ideal Transformer
$$V_p I_p = V_s I_s$$

13. Nuclear Physics

Radioactive Decay Formulas

Formulas for calculating half-life and remaining quantity in radioactive decay.

Number of Half-Lives
$$n = \frac{t}{T_{1/2}}$$
Remaining Quantity
$$N = \frac{1}{2^n} \times N_0$$

Effective Study Tips for Physics Formulas

1. Understand, Don't Just Memorize

Focus on understanding the concepts behind each formula. Know what each variable represents and the units involved.

2. Practice with Real Problems

Apply formulas to solve numerical problems. Start with simple exercises and gradually move to complex ones.

3. Create Formula Sheets

Make your own formula sheets organized by topic. The process of writing them down helps with retention.

4. Use Flashcards

Create flashcards with formulas on one side and explanations/units on the other. Review them regularly.

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