1. Mechanics
Mechanics is the branch of physics that deals with the motion of objects and the forces acting upon them. It can be divided into two main categories: kinematics and dynamics.
1.1 Kinematics
Kinematics involves the study of motion without considering the forces that cause it. The basic formulas include:
1. Displacement (\(s\)):
\[
s = s_0 + vt + \frac{1}{2}at^2
\]
where:
- \(s\) = final displacement
- \(s_0\) = initial displacement
- \(v\) = initial velocity
- \(a\) = acceleration
- \(t\) = time
2. Velocity (\(v\)):
\[
v = v_0 + at
\]
where:
- \(v\) = final velocity
- \(v_0\) = initial velocity
3. Acceleration (\(a\)):
\[
a = \frac{v - v_0}{t}
\]
4. Average Velocity (\(v_{avg}\)):
\[
v_{avg} = \frac{s}{t}
\]
1.2 Dynamics
Dynamics studies the forces and their effect on motion. The key formulas include:
1. Newton's Second Law:
\[
F = ma
\]
where:
- \(F\) = force
- \(m\) = mass
- \(a\) = acceleration
2. Weight (\(W\)):
\[
W = mg
\]
where:
- \(g\) = acceleration due to gravity (approximately \(9.81 \, m/s^2\))
3. Frictional Force (\(f\)):
\[
f = \mu N
\]
where:
- \(\mu\) = coefficient of friction
- \(N\) = normal force
4. Work (\(W\)):
\[
W = Fd \cos(\theta)
\]
where:
- \(d\) = displacement
- \(\theta\) = angle between the force and displacement direction
5. Kinetic Energy (\(KE\)):
\[
KE = \frac{1}{2}mv^2
\]
6. Potential Energy (\(PE\)):
\[
PE = mgh
\]
where:
- \(h\) = height above the ground
2. Thermodynamics
Thermodynamics is the study of heat, energy, and work. The fundamental laws and formulas include:
2.1 Laws of Thermodynamics
1. First Law of Thermodynamics:
\[
\Delta U = Q - W
\]
where:
- \(\Delta U\) = change in internal energy
- \(Q\) = heat added to the system
- \(W\) = work done by the system
2. Efficiency (\(\eta\)):
\[
\eta = \frac{W_{out}}{Q_{in}}
\]
where:
- \(W_{out}\) = work output
- \(Q_{in}\) = heat input
2.2 Ideal Gas Law
The ideal gas law relates pressure, volume, and temperature:
\[
PV = nRT
\]
where:
- \(P\) = pressure
- \(V\) = volume
- \(n\) = number of moles
- \(R\) = ideal gas constant (\(8.314 \, J/(mol \cdot K)\))
- \(T\) = temperature in Kelvin
3. Electromagnetism
Electromagnetism deals with electric charges, electric fields, magnetic fields, and their interactions. Key formulas include:
3.1 Coulomb's Law
Coulomb's law describes the force between two charged objects:
\[
F = k \frac{|q_1 q_2|}{r^2}
\]
where:
- \(F\) = force between charges
- \(k\) = Coulomb's constant (\(8.99 \times 10^9 \, N \cdot m^2/C^2\))
- \(q_1\) and \(q_2\) = charges
- \(r\) = distance between charges
3.2 Ohm's Law
Ohm's law relates voltage, current, and resistance:
\[
V = IR
\]
where:
- \(V\) = voltage
- \(I\) = current
- \(R\) = resistance
3.3 Power in Electrical Circuits
Power (\(P\)) in electrical circuits can be expressed as:
\[
P = IV
\]
Alternatively, using Ohm’s law, it can also be written as:
\[
P = I^2R \quad \text{or} \quad P = \frac{V^2}{R}
\]
4. Wave Mechanics
Wave mechanics studies the behavior of waves, including sound and light.
4.1 Wave Speed
The speed of a wave is given by:
\[
v = f\lambda
\]
where:
- \(v\) = wave speed
- \(f\) = frequency
- \(\lambda\) = wavelength
4.2 Sound Intensity Level
The intensity level of sound in decibels (dB) is calculated as:
\[
L = 10 \log_{10} \left( \frac{I}{I_0} \right)
\]
where:
- \(L\) = sound level in dB
- \(I\) = intensity of the sound
- \(I_0\) = reference intensity (\(10^{-12} \, W/m^2\))
5. Optics
Optics is the study of light and its properties.
5.1 Snell's Law
Snell's law describes the bending of light when entering a different medium:
\[
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
\]
where:
- \(n_1\) and \(n_2\) = refractive indices of the respective media
- \(\theta_1\) and \(\theta_2\) = angles of incidence and refraction
5.2 Lens Formula
The lens formula for thin lenses is:
\[
\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
\]
where:
- \(f\) = focal length
- \(d_o\) = object distance
- \(d_i\) = image distance
6. Conclusion
In summary, the basic formulas of physics serve as a foundation for understanding the laws of nature. They are applicable across various fields, from engineering to environmental science. Mastering these formulas not only aids in problem-solving but also fosters a deeper appreciation for the complexities of the universe. As we continue to explore and learn, these equations will remain critical tools in our scientific endeavors. Whether you are a student, a professional, or simply a curious mind, understanding these essential formulas is key to unlocking the mysteries of the physical world.
Frequently Asked Questions
What is the formula for Newton's second law of motion?
The formula is F = ma, where F is the force, m is the mass, and a is the acceleration.
What is the equation for gravitational potential energy?
The formula is PE = mgh, where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is height.
How do you calculate kinetic energy?
The formula for kinetic energy is KE = 1/2 mv², where KE is kinetic energy, m is mass, and v is velocity.
What is the formula for the conservation of momentum?
The formula is p_initial = p_final, where p is momentum, calculated as p = mv for each object.
What is the equation for Hooke's Law?
The formula is F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.
What is the formula for work done?
The formula is W = Fd cos(θ), where W is work, F is the force applied, d is the distance moved, and θ is the angle between the force and the direction of movement.
How do you calculate the frequency of a wave?
The formula is f = 1/T, where f is frequency and T is the period of the wave.
What is the formula for the electric force between two charges?
The formula is F = k(q₁q₂/r²), where F is the electric force, k is Coulomb's constant, q₁ and q₂ are the charges, and r is the distance between the charges.
