NMAT Physics
Complete guide to Mechanics, Waves, Electricity & Modern Physics
Mechanics
Kinematics
Key Equations of Motion
v = v₀ + at
x = x₀ + v₀t + ½at²
v² = v₀² + 2a(x - x₀)
x = x₀ + ½(v + v₀)t
Where: v = final velocity, v₀ = initial velocity, a = acceleration, t = time, x = position
Scalar Quantities
- • Distance
- • Speed
- • Mass
- • Time
- • Energy
Vector Quantities
- • Displacement
- • Velocity
- • Acceleration
- • Force
- • Momentum
Newton's Laws of Motion
1st Law (Inertia)
An object at rest stays at rest, and an object in motion stays in motion with the same velocity, unless acted upon by an unbalanced force.
2nd Law (F = ma)
The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.
F = ma (Force = mass × acceleration)
3rd Law (Action-Reaction)
For every action, there is an equal and opposite reaction.
Work, Energy, and Power
Key Formulas
Work: W = Fd cos θ (Joules)
Kinetic Energy: KE = ½mv²
Potential Energy: PE = mgh
Power: P = W/t (Watts)
Conservation: KE₁ + PE₁ = KE₂ + PE₂
Momentum
p = mv (momentum = mass × velocity)
Impulse: J = FΔt = Δp
Conservation of Momentum: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' (in collisions)
Waves & Sound
Wave Properties
Key Terms
- Wavelength (λ): Distance between two consecutive crests or troughs
- Frequency (f): Number of waves passing a point per second (Hz)
- Amplitude: Maximum displacement from equilibrium
- Period (T): Time for one complete wave cycle (T = 1/f)
- Wave Speed: v = fλ
Transverse Waves
Particles move perpendicular to wave direction
Examples: Light, water surface waves
Longitudinal Waves
Particles move parallel to wave direction
Examples: Sound waves, pressure waves
Sound
- Speed in air: ~343 m/s at 20°C
- Speed in solids: Faster than in gases
- Pitch: Related to frequency (higher f = higher pitch)
- Loudness: Related to amplitude
- Doppler Effect: Change in frequency due to relative motion
Light & Optics
Reflection
Angle of incidence = Angle of reflection
Refraction
n₁sinθ₁ = n₂sinθ₂ (Snell's Law)
Electromagnetic Spectrum
Radio → Microwave → Infrared → Visible Light → Ultraviolet → X-rays → Gamma rays
(Increasing frequency and energy →)
Electricity & Magnetism
Electric Charge & Force
Coulomb's Law
F = k(q₁q₂)/r²
k = 8.99 × 10⁹ N·m²/C²
Like charges repel, opposite charges attract
Electric Circuits
Ohm's Law
V = IR
V = Voltage (Volts), I = Current (Amperes), R = Resistance (Ohms)
Series Circuits
- • Same current through all components
- • R_total = R₁ + R₂ + R₃...
- • Voltage divides among components
Parallel Circuits
- • Same voltage across all components
- • 1/R_total = 1/R₁ + 1/R₂ + 1/R₃...
- • Current divides among branches
Power & Energy
P = IV (Power = Current × Voltage)
P = I²R = V²/R
E = Pt (Energy = Power × time)
Magnetism
- Magnetic Field: Created by moving charges or magnets
- Right-Hand Rule: Thumb = current direction, fingers = magnetic field
- Electromagnetic Induction: Changing magnetic field induces current
- Transformers: V₁/V₂ = N₁/N₂ (voltage ratio = turns ratio)
Modern Physics
Nuclear Physics
Radioactive Decay
- Alpha (α): Helium nucleus (2p + 2n), low penetration
- Beta (β): Electron or positron, medium penetration
- Gamma (γ): High-energy photon, high penetration
Half-Life
Time for half of radioactive nuclei to decay
N = N₀(½)^(t/t½)
Quantum Physics Basics
- E = hf: Energy of photon (h = Planck's constant)
- Photoelectric Effect: Light ejects electrons from metal surface
- Wave-Particle Duality: Matter exhibits both wave and particle properties
Einstein's Relativity
E = mc²
Mass and energy are equivalent; c = speed of light (3 × 10⁸ m/s)
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