Physics: Units and Measurement

• Physics is the study of matter, energy, and the fundamental forces that govern the universe.
• The Uttar Pradesh Board of High School and Intermediate Education (UP Board) prescribes the physics syllabus for classes 11 and 12.

Units and Measurement

• Physical quantities are measurable quantities that describe the physical world.
• Fundamental quantities are the base quantities that do not depend on other quantities (e.g., length, mass, time, electric current, temperature, luminous intensity, amount of substance).
• Derived quantities are defined in terms of fundamental quantities (e.g., velocity, acceleration, force, energy).
• Units are standards for measuring physical quantities.
• The International System of Units (SI) is the standard system of units used worldwide.
• SI base units: meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for temperature, candela (cd) for luminous intensity, and mole (mol) for amount of substance.
• Dimensional analysis is used to check the correctness of equations and to derive relationships between physical quantities.
• Accuracy refers to how close a measurement is to the true value.
• Precision refers to the repeatability of a measurement.
• Errors in measurement can be systematic (consistent deviations) or random (unpredictable deviations).

Kinematics

• Motion describes the change in position of an object with respect to time.
• Displacement is the change in position of an object.
• Velocity is the rate of change of displacement with respect to time.
• Average velocity is the total displacement divided by the total time interval.
• Instantaneous velocity is the velocity at a particular instant of time.
• Acceleration is the rate of change of velocity with respect to time.
• Uniform motion is motion with constant velocity (zero acceleration).
• Non-uniform motion is motion with changing velocity (non-zero acceleration).
• Equations of motion relate displacement, velocity, acceleration, and time for uniformly accelerated motion:
  • v = u + at
  • s = ut + (1/2)at^2
  • v^2 = u^2 + 2as
• Projectile motion is the motion of an object thrown into the air, subject to gravity.
• The trajectory of a projectile is a parabola.
• The horizontal range of a projectile depends on the initial velocity and the angle of projection.
• Circular motion is the motion of an object along a circular path.
• Angular displacement is the angle swept out by the radius vector of a rotating object.
• Angular velocity is the rate of change of angular displacement with respect to time.
• Angular acceleration is the rate of change of angular velocity with respect to time.
• Centripetal acceleration is the acceleration directed towards the center of the circular path, required to keep an object moving in a circle.

Laws of Motion

• Inertia is the tendency of an object to resist changes in its state of motion.
• Newton's first law states that an object at rest stays at rest, and an object in motion stays in motion with the same velocity unless acted upon by a force.
• Newton's second law states that the force acting on an object is equal to the mass of the object times its acceleration (F = ma).
• Newton's third law states that for every action, there is an equal and opposite reaction.
• Momentum is the product of an object's mass and its velocity (p = mv).
• Impulse is the change in momentum of an object.
• The law of conservation of momentum states that the total momentum of an isolated system remains constant.
• Friction is a force that opposes motion between surfaces in contact.
• Static friction prevents an object from moving when a force is applied.
• Kinetic friction opposes the motion of an object that is already moving.
• Rolling friction occurs when an object rolls over a surface.

Work, Energy, and Power

• Work is done when a force causes a displacement of an object.
• Work is calculated as the product of the force and the displacement in the direction of the force (W = Fd cos θ).
• Energy is the capacity to do work.
• Kinetic energy is the energy of motion (KE = (1/2)mv^2).
• Potential energy is stored energy due to position or configuration.
• Gravitational potential energy is the energy stored due to an object's height above the ground (PE = mgh).
• The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
• Power is the rate at which work is done (P = W/t).
• The law of conservation of energy states that energy cannot be created or destroyed, but it can be transformed from one form to another.
• Collisions can be elastic (kinetic energy is conserved) or inelastic (kinetic energy is not conserved).

Rotational Motion

• Torque is a twisting force that causes rotation.
• Moment of inertia is a measure of an object's resistance to rotational motion.
• Angular momentum is the product of an object's moment of inertia and its angular velocity (L = Iω).
• The law of conservation of angular momentum states that the total angular momentum of an isolated system remains constant.
• Rolling motion is a combination of translational and rotational motion.

Gravitation

• Newton's law of universal gravitation states that the force of attraction between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers (F = Gm1m2/r^2).
• Gravitational potential energy is the energy an object has due to its position in a gravitational field.
• Kepler's laws of planetary motion describe the motion of planets around the Sun.
  • Law of orbits: Planets move in elliptical orbits with the Sun at one focus.
  • Law of areas: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
  • Law of periods: The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
• Escape velocity is the minimum velocity required for an object to escape the gravitational pull of a planet.

Properties of Matter

• Elasticity is the ability of a solid to return to its original shape after being deformed.
• Stress is the force per unit area acting on a solid.
• Strain is the fractional deformation of a solid.
• Hooke's law states that stress is proportional to strain within the elastic limit.
• Young's modulus measures the stiffness of a solid.
• Bulk modulus measures the resistance of a solid or fluid to compression.
• Shear modulus measures the resistance of a solid to shearing forces.
• Pascal's law states that pressure applied to a fluid in a closed container is transmitted equally to every point in the fluid.
• Archimedes' principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
• Viscosity is a measure of a fluid's resistance to flow.
• Surface tension is the force that causes the surface of a liquid to contract.

Thermodynamics

• Temperature is a measure of the average kinetic energy of the particles in a substance.
• Heat is the transfer of energy due to a temperature difference.
• Specific heat capacity is the amount of heat required to raise the temperature of one unit mass of a substance by one degree Celsius.
• The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system (ΔU = Q - W).
• The second law of thermodynamics states that the entropy of an isolated system always increases or remains constant.
• Heat engines convert thermal energy into mechanical work.
• Refrigerators transfer heat from a cold reservoir to a hot reservoir.

Oscillations and Waves

• Simple harmonic motion (SHM) is a periodic motion in which the restoring force is proportional to the displacement.
• A wave is a disturbance that propagates through a medium, transferring energy without transferring matter.
• Transverse waves are waves in which the particles of the medium move perpendicular to the direction of wave propagation (e.g., light waves).
• Longitudinal waves are waves in which the particles of the medium move parallel to the direction of wave propagation (e.g., sound waves).
• Wavelength is the distance between two consecutive crests or troughs of a wave.
• Frequency is the number of waves that pass a point per unit time.
• The speed of a wave depends on the properties of the medium.
• Superposition of waves is the phenomenon where two or more waves combine to form a resultant wave.
• Interference is the superposition of waves from coherent sources, resulting in constructive or destructive interference.
• Diffraction is the bending of waves around obstacles or through openings.
• Polarization is the phenomenon where the vibrations of a transverse wave are restricted to one plane.
• Doppler effect is the change in frequency of a wave observed by a moving observer or source.

An overview of units and measurement in physics, according to the Uttar Pradesh Board syllabus. It defines fundamental and derived quantities with examples. It also introduces the International System of Units (SI) and its base units.