Physics formula for all in one

 Comprehensive Guide to Physics Formulas

Physics is the study of the natural world and its fundamental principles. It encompasses a wide range of topics from the microscopic scale (quantum mechanics) to the cosmic scale (cosmology). To describe and quantify physical phenomena, scientists and engineers use a variety of formulas. These formulas are essential tools that help us understand how the universe works. In this article, we will explore the most important physics formulas across various branches of physics, providing a comprehensive overview.

1. Mechanics Formulas

Mechanics is the branch of physics that deals with the motion of objects and the forces acting upon them. This section will cover the fundamental formulas that describe the motion of objects, from simple linear motion to rotational motion.

1.1 Newton’s Laws of Motion

Newton’s three laws of motion are the foundation of classical mechanics.

First Law (Law of Inertia):

An object will remain at rest or in uniform motion unless acted upon by an external force.

Second Law (Force and Acceleration):

𝐹

=

𝑚

𝑎

F=ma

Where:

𝐹

F = Force (in newtons, N)

𝑚

m = Mass (in kilograms, kg)

𝑎

a = Acceleration (in meters per second squared, m/s²)

Third Law (Action and Reaction):

For every action, there is an equal and opposite reaction.

1.2 Kinematic Equations (For Uniform Acceleration)

Kinematics deals with the motion of objects without considering the forces causing the motion. These equations are used when acceleration is constant.

Velocity-time equation:

𝑣

=

𝑢

+

𝑎

𝑡

v=u+at

Where:

𝑣

v = Final velocity (in m/s)

𝑢

u = Initial velocity (in m/s)

𝑎

a = Acceleration (in m/s²)

𝑡

t = Time (in seconds)

Displacement equation:

𝑠

=

𝑢

𝑡

+

1

2

𝑎

𝑡

2

s=ut+ 

2

1

 at 

2

 

Where:

𝑠

s = Displacement (in meters)

𝑢

u = Initial velocity (in m/s)

𝑎

a = Acceleration (in m/s²)

𝑡

t = Time (in seconds)

Velocity-displacement equation:

𝑣

2

=

𝑢

2

+

2

𝑎

𝑠

v 

2

 =u 

2

 +2as

Where:

𝑣

v = Final velocity (in m/s)

𝑢

u = Initial velocity (in m/s)

𝑎

a = Acceleration (in m/s²)

𝑠

s = Displacement (in meters)

1.3 Work, Energy, and Power

Work and energy are key concepts in mechanics, and power is the rate at which work is done.

Work:

𝑊

=

𝐹

𝑑

cos

⁡

𝜃

W=Fdcosθ

Where:

𝑊

W = Work (in joules, J)

𝐹

F = Force (in newtons, N)

𝑑

d = Displacement (in meters)

𝜃

θ = Angle between force and displacement (in degrees)

Kinetic Energy:

𝐾

𝐸

=

1

2

𝑚

𝑣

2

KE= 

2

1

 mv 

2

 

Where:

𝐾

𝐸

KE = Kinetic energy (in joules, J)

𝑚

m = Mass (in kilograms, kg)

𝑣

v = Velocity (in m/s)

Potential Energy:

𝑃

𝐸

=

𝑚

𝑔

ℎ

PE=mgh

Where:

𝑃

𝐸

PE = Potential energy (in joules, J)

𝑚

m = Mass (in kilograms, kg)

𝑔

g = Acceleration due to gravity (

9.8

 

m/s

2

9.8m/s 

2

 )

ℎ

h = Height (in meters)

Power:

𝑃

=

𝑊

𝑡

P= 

t

W

 

Where:

𝑃

P = Power (in watts, W)

𝑊

W = Work done (in joules, J)

𝑡

t = Time taken (in seconds)

1.4 Rotational Motion

Rotational motion involves objects that rotate around an axis, and similar to linear motion, it has its own set of kinematic and dynamic equations.

Angular Displacement:

𝜃

=

𝜃

0

+

𝜔

0

𝑡

+

1

2

𝛼

𝑡

2

θ=θ 

0

 +ω 

0

 t+ 

2

1

 αt 

2

 

Where:

𝜃

θ = Angular displacement (in radians)

𝜔

0

ω 

0

  = Initial angular velocity (in radians per second)

𝛼

α = Angular acceleration (in radians per second squared)

𝑡

t = Time (in seconds)

Torque:

𝜏

=

𝐼

𝛼

τ=Iα

Where:

𝜏

τ = Torque (in newton-meters, N·m)

𝐼

I = Moment of inertia (in kg·m²)

𝛼

α = Angular acceleration (in radians per second squared)

Moment of Inertia (for point mass):

𝐼

=

𝑚

𝑟

2

I=mr 

2

 

Where:

𝐼

I = Moment of inertia (in kg·m²)

𝑚

m = Mass (in kilograms)

𝑟

r = Distance from the axis of rotation (in meters)

2. Gravitation Formulas

Gravitation is the force that attracts objects toward one another. The most fundamental formula in gravitation is Newton's Law of Universal Gravitation.

Newton's Law of Universal Gravitation:

𝐹

=

𝐺

𝑚

1

𝑚

2

𝑟

2

F=G 

r 

2

 

m 

1

 m 

2

 

 

Where:

𝐹

F = Gravitational force (in newtons, N)

𝐺

G = Gravitational constant (

6.674

×

10

−

11

 

N

\cdotp

m

2

/

kg

2

6.674×10 

−11

 N\cdotpm 

2

 /kg 

2

 )

𝑚

1

m 

1

  and 

𝑚

2

m 

2

  = Masses of the two objects (in kilograms)

𝑟

r = Distance between the objects (in meters)

Gravitational Potential Energy:

𝑃

𝐸

=

−

𝐺

𝑚

1

𝑚

2

𝑟

PE=−G 

r

m 

1

 m 

2

 

 

Where:

𝑃

𝐸

PE = Gravitational potential energy (in joules, J)

𝑚

1

m 

1

  and 

𝑚

2

m 

2

  = Masses of the two objects (in kilograms)

𝑟

r = Distance between the objects (in meters)

3. Thermodynamics Formulas

Thermodynamics is the study of heat and energy transfer, and it plays a crucial role in understanding the behavior of gases, engines, and energy systems.

First Law of Thermodynamics:

Δ

𝑈

=

𝑄

−

𝑊

ΔU=Q−W

Where:

Δ

𝑈

ΔU = Change in internal energy (in joules, J)

𝑄

Q = Heat added to the system (in joules, J)

𝑊

W = Work done by the system (in joules, J)

Ideal Gas Law:

𝑃

𝑉

=

𝑛

𝑅

𝑇

PV=nRT

Where:

𝑃

P = Pressure (in pascals, Pa)

𝑉

V = Volume (in cubic meters, m³)

𝑛

n = Number of moles of gas

𝑅

R = Ideal gas constant (

8.31

 

J/mol

\cdotp

K

8.31J/mol\cdotpK)

𝑇

T = Temperature (in kelvins, K)

Specific Heat Capacity:

𝑄

=

𝑚

𝑐

Δ

𝑇

Q=mcΔT

Where:

𝑄

Q = Heat energy transferred (in joules, J)

𝑚

m = Mass (in kilograms, kg)

𝑐

c = Specific heat capacity (in J/kg·K)

Δ

𝑇

ΔT = Change in temperature (in kelvins, K)

4. Electricity and Magnetism Formulas

Electricity and magnetism are two fundamental aspects of electromagnetism. Below are key formulas that describe the behavior of electrical circuits and magnetic fields.

Ohm's Law:

𝑉

=

𝐼

𝑅

V=IR

Where:

𝑉

V = Voltage (in volts, V)

𝐼

I = Current (in amperes, A)

𝑅

R = Resistance (in ohms, Ω)

Coulomb’s Law:

𝐹

=

𝑘

𝑒

𝑞

1

𝑞

2

𝑟

2

F=k 

e

  

r 

2

 

q 

1

 q 

2

 

 

Where:

𝐹

F = Electrostatic force (in newtons, N)

𝑘

𝑒

k 

e

  = Coulomb’s constant (

8.99

×

10

9

 

N

\cdotp

m

2

/

C

2

8.99×10 

9

 N\cdotpm 

2

 /C 

2

 )

𝑞

1

q 

1

  and 

𝑞

2

q 

2

  = Charges (in coulombs, C)

𝑟

r = Distance between charges (in meters)

Magnetic Force on a Moving Charge:

𝐹

=

𝑞

𝑣

𝐵

sin

⁡

𝜃

F=qvBsinθ

Where:

𝐹

F = Magnetic force (in newtons, N)

𝑞

q = Charge (in coulombs, C)

𝑣

v = Velocity (in meters per second, m/s)

𝐵

B = Magnetic field strength (in teslas, T)

𝜃

θ = Angle between the velocity and magnetic field

5. Wave and Optics Formulas

Waves and optics deal with the behavior of light, sound, and other wave phenomena.

Wave Speed:

𝑣

=

𝑓

𝜆

v=fλ

Where:

𝑣

v = Wave speed (in meters per second, m/s)

𝑓

f = Frequency (in hertz, Hz)

𝜆

λ = Wavelength (in meters)

Snell’s Law of Refraction:

𝑛

1

sin

⁡

𝜃

1

=

𝑛

2

sin

⁡

𝜃

2

n 

1

 sinθ 

1

 =n 

2

 sinθ 

2

 

Where:

𝑛

1

n 

1

  and 

𝑛

2

n 

2

  = Refractive indices of the two media

𝜃

1

θ 

1

  and 

𝜃

2

θ 

2

  = Angles of incidence and refraction (in degre

es)

Lens Formula:

1

𝑓

=

1

𝑣

−

1

𝑢

f

1

 = 

v

1

 − 

u

1

 

Where:

𝑓

f = Focal length (in meters)

𝑣

v = Image distance (in meters)

𝑢

u = Object distance (in meters)

Conclusion

This comprehensive list of physics formulas covers essential concepts in mechanics, gravitation, thermodynamics, electricity and magnetism, and wave and optics theory. Mastering these formulas allows you to understand and analyze the physical world around us. Each formula represents a fundamental law or principle that has been established over centuries, and they are indispensable tools for solving real-world problems in physics.