Mechanics: Newton's Laws and Energy Concepts

Mechanics

• Newton's Laws of Motion:
• First Law: A body continues in a state of rest or uniform motion in a straight line unless acted upon by a resultant force.
• Second Law: The rate of change of momentum of a body is directly proportional to the resultant force acting on it and takes place in the direction in which the force acts. (F = ma)
• Third Law: To every action, there is an equal and opposite reaction.
• Work, Energy, and Power:
• Work is done when a force causes a displacement in the direction of the force. (W = F * d * cosθ)
• Kinetic Energy is the energy of motion (KE = 1/2mv²).
• Potential Energy is the energy of position (PE = mgh).
• Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another.
• Power is the rate at which work is done (P = W/t).
• Circular Motion:
• Uniform Circular Motion: Motion in a circle at a constant speed.
• Centripetal Force: Force that acts towards the center of the circle, keeping the object in circular motion.
• Centrifugal Force: Fictitious force apparent to an observer in a rotating frame of reference.
• Gravitation:
• Newton's Law of Universal Gravitation: Every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. (F = Gm₁m₂/r²)
• Gravitational field strength is the force per unit mass at a point in a gravitational field.
• Kepler's Laws of Planetary Motion: describe the motion of planets around the Sun.

Oscillations

• Simple Harmonic Motion (SHM):
• Definition: A periodic motion where the restoring force is proportional to the displacement from the equilibrium position and directed towards it.
• Characteristics: Repetitive, periodic, and involves acceleration proportional to displacement.
• Examples: Simple pendulum, mass-spring system.
• Characteristics of SHM:
• Displacement as a sinusoidal function of time.
• Velocity is maximum at the mean position and zero at the extreme positions.
• Acceleration is maximum at the extreme positions and zero at the mean position.

Waves

• Types of Waves:
• Transverse waves: Displacement is perpendicular to the direction of wave propagation (e.g., light waves).
• Longitudinal waves: Displacement is parallel to the direction of wave propagation (e.g., sound waves).
• Wave Properties:
• Amplitude: Maximum displacement from the equilibrium position.
• Wavelength: Distance between two consecutive crests or troughs.
• Frequency: Number of oscillations per unit time.
• Period: Time taken for one complete oscillation.
• Speed: Rate at which the wave propagates.
• Wave Interactions:
• Reflection: Bouncing of a wave off a surface.
• Refraction: Bending of a wave as it passes from one medium to another.
• Diffraction: Spreading of a wave as it passes through an opening or around an obstacle.
• Interference: Resultant wave formed by the superposition of two or more waves.

Thermodynamics

• Thermal Properties of Matter:
• Heat capacity: Amount of heat required to raise the temperature of a substance by 1 °C.
• Specific heat capacity: Heat capacity per unit mass of a substance.
• Latent heat: Heat absorbed or released during a change of state without a change in temperature.
• Laws of Thermodynamics:
• Zeroth Law: If two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other.
• First Law: Energy can be transferred and transformed, but it cannot be created or destroyed.
• Second Law: The total entropy of an isolated system can only increase over time, or remain constant in ideal cases (reversible processes).
• Third Law: The entropy of a perfect crystal approaches zero as the temperature approaches absolute zero (0 K).

Electricity and Magnetism

• Electric Charges and Fields:
• Properties of electric charges: Conservation, quantization, and attracting or repelling.
• Coulomb's Law: Force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
• Electric Potential and Capacitance:
• Electric potential difference: Work done per unit charge to move a charge from one point to another.
• Capacitance: Ability of a capacitor to store electric charge.

Modern Physics

• Photoelectric Effect:
• Einstein's explanation of the photoelectric effect: Light behaves as a stream of photons.

Atomic Structure

• Bohr Model of Hydrogen Atom:
• Electrons orbit the nucleus in specific energy levels, with quantized angular momentum.

Nuclei

• Radioactivity:
• Types of radioactive decay (alpha, beta, gamma).
• Radioactive decay law (exponential decay).
• Nuclear Reactions:
• Fission: Splitting of a heavy nucleus into smaller nuclei.
• Fusion: Combining of lighter nuclei into a heavier nucleus.