Mechanics

Time period, frequency, and amplitude

  1. Simple Harmonic Motion (SHM) is a type of oscillatory motion where the restoring force is proportional to displacement and acts in the opposite direction.
  2. The time period (T) of SHM is the time taken to complete one full oscillation.
  3. The frequency (f) is the number of oscillations completed in one second.
  4. The relationship between time period and frequency is given by f = 1/T.
  5. The amplitude (A) is the maximum displacement of the oscillating particle from its equilibrium p

Oscillations, pendulums, and springs

  1. Oscillation is the repetitive motion of a system about its equilibrium position.
  2. Simple Harmonic Motion (SHM) is a special type of oscillation where the restoring force is proportional to displacement and acts in the opposite direction.
  3. A system undergoing SHM exhibits a periodic motion with constant frequency and time period.
  4. The motion of a simple pendulum and a mass attached to a spring are classic examples of SHM.
  5. The equation of motion for SHM is F = -kx

Definitions and characteristics of Simple Harmonic Motion (SHM)

  1. Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction.
  2. The equation governing SHM is F = -kx, where F is the restoring force, k is the force constant, and x is the displacement from equilibrium.
  3. In SHM, the motion occurs around a fixed equilibrium position.
  4. The restoring force in SHM is responsible for bringing the object back to its equilibrium position.
  5. SHM is a form of

Satellites: artificial satellites and applications

  1. An artificial satellite is a man-made object placed into orbit around a celestial body, primarily Earth.
  2. Artificial satellites are launched using rockets or space vehicles.
  3. They remain in orbit due to the balance between the gravitational pull of the Earth and their centripetal force.
  4. Satellites follow the laws of orbital motion as described by Kepler and Newton.
  5. The orbital velocity of a satellite depends on its altitude and the mass of the central body.
  6. Low Ear

Gravitational potential energy, escape velocity, orbital velocity

  1. Gravitational Potential Energy (U) is the energy possessed by an object due to its position in a gravitational field.
  2. The formula for gravitational potential energy is U = -G(m₁m₂ / r), where G is the gravitational constant, m₁ and m₂ are the masses, and r is the distance between their centers.
  3. The negative sign in U indicates that gravitational force is attractive, and energy must be supplied to separate the masses.
  4. The gravitational potential at a point is defined as the potential energy per u

Acceleration due to gravity, variation with altitude and depth

  1. The acceleration due to gravity (g) is the acceleration experienced by an object due to the gravitational pull of the Earth.
  2. The standard value of g at the Earth's surface is approximately 9.8 m/s².
  3. g is calculated using the formula g = GM/R², where G is the gravitational constant, M is the Earth's mass, and R is its radius.
  4. The value of g is maximum at the Earth’s surface and decreases with altitude, depth, and latitude.
  5. At higher altitudes, g decreases because the dist

Newton’s law of gravitation

  1. Newton’s Law of Gravitation states that every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
  2. The mathematical expression for gravitational force is F = G (m₁m₂ / r²), where G is the gravitational constant, m₁ and m₂ are the masses, and r is the distance between the centers of the masses.
  3. The gravitational constant (G) has a value of approximately 6.674 × 10⁻¹¹ N·m²/kg² in SI un

Conservation of energy, power

  1. The Law of Conservation of Energy states that energy can neither be created nor destroyed, only transformed from one form to another.
  2. In an isolated system with no external forces, the total energy remains constant.
  3. Mechanical energy, the sum of kinetic energy (KE) and potential energy (PE), is conserved in systems with no non-conservative forces like friction.
  4. In real-world systems, some energy is converted into heat or other non-mechanical forms due to dissipative forces.

Work-energy theorem, types of energy (kinetic, potential, etc.)

  1. The Work-Energy Theorem states that the work done by all forces acting on an object is equal to the change in its kinetic energy.
  2. The mathematical expression for the Work-Energy Theorem is W = ΔKE, where W is work and ΔKE is the change in kinetic energy.
  3. Kinetic Energy (KE) is the energy of an object due to its motion, given by KE = ½ mv², where m is mass and v is velocity.
  4. Potential Energy (PE) is the energy stored in an object due to its position or configuration.
  5. The formula for gravi

Definitions and units

  1. Work is done when a force is applied to an object, and the object moves in the direction of the applied force.
  2. The mathematical formula for work is W = F × d × cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and displacement.
  3. The SI unit of work is the joule (J), where 1 joule = 1 newton × 1 meter.
  4. Positive work occurs when the force and displacement are in the same direction.
  5. Negative work occurs when the force
Mechanics