(5) Complete Class 12th PHYSICS in 1 Shot | Maha Revision - JEE Main 2024

Detailed Physics Revision Notes for JEE

1. Kinematics

• Displacement: The shortest distance from the initial to the final position of an object. It is a vector quantity, meaning it has both magnitude and direction.

• Velocity: Defined as displacement per unit time. The formula for average velocity is:

  • Average Velocity = (Displacement) / (Time interval)

  • For uniform acceleration: v = u + at (where v = final velocity, u = initial velocity, a = acceleration, and t = time)

• Acceleration: The rate of change of velocity with respect to time. It can be uniform (constant) or variable (changing).

• Equations of Motion:

  • v = u + at

  • s = ut + (1/2)at²

  • v² = u² + 2as

    • Where:

      • s = displacement

      • u = initial velocity

      • v = final velocity

      • a = acceleration

      • t = time.

2. Laws of Motion

• Newton's First Law: An object will maintain its current state of motion (at rest or in uniform motion in a straight line) unless acted upon by a net external force.

• Newton's Second Law: Given by the equation F = ma; where F is the net force acting on the object, m is the mass, and a is the acceleration produced.

• Newton's Third Law: States that for every action, there is an equal and opposite reaction; forces always occur in pairs.

• Applications: Understanding concepts of friction, tension, normal forces, and the influence of these forces in various scenarios.

3. Work, Energy, and Power

• Work Done: The work done by a constant force can be calculated by W = F × d × cos(θ), where θ is the angle between the force and the direction of motion.

• Kinetic Energy (KE): Given by the formula KE = (1/2)mv²; this is the energy possessed by an object due to its motion.

• Potential Energy (PE): The energy stored in an object because of its position in a gravitational field, calculated as PE = mgh (where m is mass, g is gravitational acceleration, and h is height).

• Mechanical Energy: The total mechanical energy of a system is the sum of kinetic and potential energies: Total Mechanical Energy = KE + PE.

• Power: Defined as the rate at which work is done. The formula for power is P = W/t, where W is the work done and t is the time interval.

4. System of Particles and Rotational Motion

• Center of Mass: The average position of all the mass in a system. For a system of particles:

  • R_cm = (m₁r₁ + m₂r₂ + m₃r₃) / (m₁ + m₂ + m₃)

• Torque: Denoted as τ, it is the rotational equivalent of force and is given by τ = r × F, where r is the distance from the pivot point to where the force is applied. Torque depends on both the magnitude of the force and the distance to the pivot.

• Moment of Inertia (I): Given by the formula I = ∑mr² (where m is mass and r is the distance from the axis of rotation). This quantity plays a similar role for rotational motion as mass does for linear motion.

• Angular Momentum (L): Defined as L = Iω (where ω is angular velocity). Angular momentum is conserved in closed systems where no external torques are acting.

5. Gravitation

• Law of Gravitation: States that any two masses attract each other with a force (F) that is proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers:

  • F = G(m₁ * m₂)/r² (where G = 6.674 × 10⁻¹¹ N(m/kg)² is the gravitational constant)

• Acceleration due to Gravity (g): Given by the formula g = G(m₁/r²), where m₁ is the mass of the Earth, and r is the distance from the center of the Earth.

• Gravitational Potential Energy (PE): Calculated as PE = -G(m₁m₂/r), reflecting the work done against gravitational forces.

6. Properties of Matter

• Density (ρ): Defined as ρ = m/V; represents mass per unit volume of a substance, a key property in material science.

• Pressure (P): Calculated as P = F/A; the force applied per unit area, an important concept in fluid mechanics.

• Buoyant Force: According to Archimedes' principle, the upward force exerted by a fluid on a submerged object is equal to the weight of the fluid displaced.

• Viscosity: Refers to a fluid's resistance to flow, crucial in understanding fluid dynamics and interaction of fluids with solid boundaries.

7. Thermodynamics

• Zeroth Law of Thermodynamics: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other, leading to the concept of temperature.

• First Law of Thermodynamics: Expressed as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.

• Second Law of Thermodynamics: States that the entropy of an isolated system tends to increase; heat cannot spontaneously flow from a colder to a hotter body.

• Carnot Engine: An ideal heat engine that operates on the reversible Carnot cycle, defining maximum possible efficiency among heat engines.

8. Waves and Oscillations

• Simple Harmonic Motion (SHM): A type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction.

• Equation of SHM: x(t) = Acos(ωt + φ), where A is amplitude, ω is angular frequency, and φ is phase constant.

• Wave Properties:

  • Amplitude: Maximum displacement from the equilibrium position.

  • Wavelength (λ): Distance between two consecutive crests or troughs in a wave.

  • Frequency (f): Number of oscillations per unit time (measured in Hertz).

• Wave Equation: v = fλ (where v = wave speed, f = frequency, λ = wavelength).

9. Optics

• Reflection: The process in which light rays bounce back when they hit a reflective surface.

  • Laws of Reflection: The angle of incidence equals the angle of reflection (θ₁ = θ₂).

• Refraction: The bending of light as it passes from one medium to another; described by Snell's Law: n₁sin(θ₁) = n₂sin(θ₂), where n is the refractive index of the respective media.

• Lens Formula & Magnification:

  • Lens Formula: 1/f = 1/v - 1/u

    • Where f is the focal length, v is the image distance, and u is the object distance.

  • Magnification (m): Defined as m = h'/h = v/u (where h' is image height, h is object height).

10. Electromagnetism

• Coulomb's Law: Describes the electrostatic force between two charges:

  • F = k(q₁ * q₂)/r², where k is Coulomb's constant.

• Electric Field (E): Defined as E = F/q; represents the force per unit charge acting on a positive test charge placed in the field.

• Ohm's Law: Expressed as V = IR; where V is the potential difference, I is the current, and R is the resistance.

• Faraday's Law of Electromagnetic Induction: States that the induced electromotive force (emf) in a circuit is proportional to the rate of change of magnetic flux through the circuit.

11. Modern Physics

• Photoelectric Effect: Given by the equation E = hf; indicates that light can eject electrons from a material if it possesses enough frequency, showing the particle-like behavior of light (Planck's quantum theory).

• Nuclear Reactions: Involves processes that change an atom's nucleus, including:

  • Fission: The splitting of a nucleus into smaller parts.

  • Fusion: Combining of lighter nuclei to form a heavier nucleus, as observed in stars.

• Half-Life: The time required for half of a radioactive substance to decay; calculated using the decay constant (λ): t₁/₂ = ln(2)/λ.

Study Recommendations:

• Regularly review concepts and solve numerical problems to strengthen understanding.

• Practice problem-solving under timed conditions to prepare for the exam effectively.

• Focus on understanding the derivations, their applications, and deep comprehension of physical concepts to enhance analytical skills.