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
$$\text{Multiply speed with } \frac{10}{36}$$

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. Temperature Conversions

Temperature Scale Conversions

These formulas allow conversion between different temperature scales: Celsius, Fahrenheit, and Kelvin.

Celsius to Fahrenheit
$$T_F = \frac{9}{5} T_c + 32$$
Celsius to Fahrenheit
$$T_F = 1.8 T_c + 32$$
Celsius to Kelvin
$$T_K = 273 + T_C$$

Study Tips for Physics Formulas

  • Understand, don't just memorize: Learn the derivation and meaning behind each formula
  • Practice regularly: Solve numerical problems using these formulas daily
  • Create flashcards: Write formulas on one side and explanations on the other
  • Group related formulas: Study formulas by topic rather than randomly
  • Check units: Always verify that units are consistent in calculations
  • Review before exams: Go through this sheet regularly to keep formulas fresh in memory

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