Physics Essentials: Vibrations, Waves, Gravity, Fields, Optics
Vibratory Motion (MAS) – Radians
X(t) = a sin (wt + fi), A = xmax
w = 2π / T = 2πnu, nu = 1/T = 1/nu
vtransversal = dx / dt
a = –w2 · x
x = Acoswt = acos (wt + π/2)
v = Awcos (wt + fi), vmax = Aw
v = ±w · √(A2–x2)
F = –kx, K = Mw2-√ w = k / m (kN/m)
Simple Pendulum – Theta
θ = s / l
T = 2π · √(L / g)
s = θ x L
cos θ = Lh / L
w = √(g / L)
θ(t) = θm sin (wt + fi) – fi then removed
Energy of an Oscillator
Ec = 1/2mv2
Ep = Ep(x), W = Ep
For a Spring
Ep = 1/2kx2
Ec = 1/2mv2
Et = Ep + Ec = constant
In the
Read MoreFaraday’s Experiments and Electromagnetic Induction
Faraday’s Experiences
The English physicist and chemist M. Faraday experimentally obtained an electrical current from magnetism in 1831. These are his stories:
- First experience: moving a magnet inside a coil. If approaching the magnet to a coil, an induced current occurs during the movement of the magnet. The direction of the induced current is reversed if the magnet moves away. With a fixed coil and magnet, no induced current is observed. The same results are obtained if we keep the magnet fixed
Understanding Oscillatory Motion and Wave Phenomena
Simple Harmonic Motion (SHM)
Simple harmonic motion is a straight-line oscillatory motion where the restoring force is proportional to the displacement and acts in the opposite direction. Key features include:
- Oscillation/Vibration
- Oscillation Center (O)
- Elongation (X)
- Amplitude (A) – always positive
- Period (T)
- Frequency (F) = 1/T
- Angular Frequency (ω)
Dynamics of SHM
-k: Restoring force constant
-F: Central force, proportional to displacement (r)
-T: Period depends on mass (m) and k, not amplitude (A)
Waves
A
Read MoreFundamentals of Electricity: Charge, Current, and Voltage
Electricity: Powering Modern Life
Electricity is crucial for modern life, enabling lighting, television, music, and electrical appliances. Without it, our world would nearly grind to a halt.
What is Electricity?
Electricity is a natural interaction originating in the elementary particles forming atoms. The term derives from the Greek word elektron (amber).
Electric Charge
- Electric Charge: An intrinsic property of elementary particles, like mass. Electrons have a negative charge, and protons have a positive
Gravity, Spacetime, and Motion Fundamentals
Gravity & Spacetime
Laws of Physics are determined by:
1. Size: Big & Small
2. Speed: Fast & Slow
- Larger than 10-9m (big)
- Smaller than 10-9m (small)
- Comparable to 3×108m/s (fast)
- Slower than 3×108m/s (slow)
- Classical Mechanics (big & slow)
- Quantum Mechanics (small & slow)
- Relativistic Mechanics (fast & large)
- Quantum Field Theory (small & fast)
General Relativity
- Space & time form a 4D “fabric”
- Can be curved by mass & energy
Gravitation is not a force but a curvature of
Read MoreUnderstanding Electrical Power, Loads, and Magnetism
Electrical Power
Electrical power is the rate at which electrical energy is transferred by an electric circuit. Electric current is the orderly movement of electric charges through a material. These moving charges carry electrical energy, which can be transformed into other forms of energy such as light, heat, or motion. The greater the flow of charge through a material, the stronger the current.
Conductors and Insulators
Materials vary in their ability to conduct electricity. Conductors are materials
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