Kinematics and Measurement Concepts

Definitions

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Measurements

• Homogeneity of Equations: Every term on both sides of the equal sign must have the same units.
• Systematic Errors: Readings or measurements are consistently smaller or larger than the true value by a fixed amount.
• Random Errors: Readings or measurements vary around a mean value.
• Accuracy: How close the average measurement is to the true value. Affected by systematic error.
• Precision: How well repeated measurements agree with each other. Affected by random error.
• Scalar: A quantity with only magnitude..
• Vector: A quantity with both magnitude and direction.

Kinematics

• Distance: The length of the path an object travels.
• Displacement: The distance moved in a specified direction from a reference point.
• Speed: The rate of change of distance with respect to time, instantaneous speed is the rate at which distance is changing at any given time, average speed is the total distance divided by the total time taken,
• Velocity: The rate of change of displacement with respect to time. It has direction. Average is total displacement divided by total time.
• Acceleration: The rate of change of velocity with respect to time. Average is change in velocity over time.

Dynamics

• Newton's 1st Law of Motion: A body continues in its state of rest or uniform motion in a straight line unless compelled to change that state by a resultant force acting upon it.
• Inertia: A body's reluctance to change its motion. Mass is a measure of inertia.
• Weight: The gravitational force exerted on an object.
• Equilibrium: The resultant force and torque are both zero.
• Newton's 3rd Law of Motion: For every action, there is an equal and opposite reaction.
• Momentum: Mass × velocity
• Newton's 2nd Law of Motion: The rate of change of momentum of a body is directly proportional to the resultant force acting on it and takes place in the same direction as the force.
• Impulse: Force × time
• Conservation of Momentum: In a closed system, the total momentum remains constant.
• Elastic Collision: Total momentum and kinetic energy are conserved.
• Inelastic Collision: Total momentum is conserved, but kinetic energy is lost.
• Perfectly Inelastic Collision: Total momentum is conserved, and the colliding objects stick together.
• Head-On Collision: The center of mass of the objects are on a single line before and after the collision.

Forces

• Hooke's Law: The extension of a spring is proportional to the applied force up to the limit of proportionality.
• Density: Mass per unit volume.
• Pressure: Force per unit area acting perpendicular to the area.
• Upthrust: The upward force exerted on an object by a fluid.
• Archimedes' Principle: The upthrust on a submerged object is equal to the weight of fluid displaced.
• Equilibrium: The resultant force and torque are both zero.
• Principle of Moments: The sum of clockwise moments equals the sum of anticlockwise moments about a point.
• Moment: The product of force and the perpendicular distance from the pivot to the line of action of the force.
• Couple: Two equal and opposite forces that do not act along the same line.
• Torque of a couple: The product of one force and the perpendicular distance between the two forces.
• Center of Gravity: The point at which the weight of an object appears to act.

Work, Energy, Power

• Work Done: Force × displacement in the direction of the force.
• Joule: The unit of work (and energy).
• Principle of Conservation of Energy: Energy in an isolated system remains constant; it may change forms but the total amount remains fixed.
• Power: Rate of work done or energy conversion.

Circular Motion

• Angular Displacement: Angle object makes relative to a reference line.
• Radian: Angle subtended by an arc length equal to the radius of the arc.
• Angular Velocity: Rate of change of angular displacement with respect to time.
• Period: Time for one complete revolution.
• Frequency: Number of complete revolutions per unit time.

Gravitational Field

• Newton's Law of Gravitation: The force of attraction between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Gravitational Field: A region of space where a mass experiences a gravitational force.
• Gravitational Field Strength: Gravitational force per unit mass.
• Gravitational Potential Energy: Work done to move a mass from infinity to a point in the field without acceleration.
• Gravitational Potential: Work done per unit mass to move a mass from infinity to a point in the field without acceleration.
• Geostationary Satellite: A satellite that remains fixed above a particular location on Earth's surface. Orbital period matches Earth's rotation.

Oscillations

• Simple Harmonic Motion: Acceleration is directly proportional to displacement from equilibrium and acts in the opposite direction.
• Angular Frequency: Rate of change of phase angle.
• Amplitude: Maximum displacement from equilibrium.
• Period: Time for one complete oscillation.
• Frequency: Number of oscillations per unit time.
• Free Oscillations: Oscillations without any external driving or resistive forces.
• Damped Oscillations: Oscillations with energy loss over time.
• Light Damping: Amplitude decays exponentially with time.
• Critical Damping: System returns to equilibrium in the shortest possible time without oscillations.
• Heavy Damping: System takes a long time to return to equilibrium with no oscillations.
• Forced Oscillations: Oscillations driven by an external periodic force.
• Resonance: Driving frequency matches natural frequency, resulting in maximum amplitude.

Wave Motion

• Progressive Wave: Transfers energy without matter transfer by a disturbance.
• Displacement: Distance a particle is displaced from its equilibrium position,
• Amplitude: Maximum displacement from equilibrium.
• Period: Time for one complete oscillation.
• Frequency: Number of oscillations per unit time.
• Wavelength: Distance between consecutive points on the wave in phase.
• Wave Speed: Distance travelled by the wave per unit time.
• Phase: Stage of motion in a cycle. Expressed as angle in radians.
• Phase Difference: Difference in phase between two points on a wave.
• Wavefront: Line or surface containing points that are in phase.
• Wave Intensity: Rate of energy transfer per unit area to objects perpendicular to the propagation direction.
• Point Source: Source emitting waves radially outward.

Transverse and Longitudinal Waves

• Transverse Wave: Particles oscillate perpendicular to energy transfer direction.
• Longitudinal Wave: Particles oscillate parallel to energy transfer direction
• Polarization: Restriction of oscillations in a transverse wave to a single plane.
• Malus' Law: Intensity of polarized light passing through a polarizer varies with the square of the cosine of the angle between the polarizer and the vibration direction.

Superposition

• Principle of Superposition: Resultant displacement is the vector sum of individual waves' displacements.
• Stationary Wave: Superposition of two progressive waves traveling in opposite directions, resulting in nodes and antinodes.
• Diffraction: Spreading of waves after passing through an opening or around an obstacle. Affected by the relative sizes of the opening and the wavelength.
• Coherence: Waves with a constant phase difference.
• Interference: Superposition of two or more coherent waves.
• Constructive Interference: Waves add up to give a larger amplitude.
• Destructive Interference: Waves cancel out to give a smaller amplitude.
• Path Difference: Difference in distances waves travel from their source to a point.

Thermal Physics

• Heat: Energy transferred between objects due to temperature differences.
• Thermal Equilibrium: No net heat flow between objects at the same temperature.
• Zeroth Law of Thermodynamics: If two systems are in thermal equilibrium with a third, then they are in thermal equilibrium with each other.
• Ideal Gas: Obeys the equation pV=nRT.
• Mole: Amount of substance containing Avogadro's number of particles.

Thermal Physics 2: First Law

• Heat Capacity: Quantity of heat required to raise temperature by 1°C without phase change.
• Specific Heat Capacity: Quantity of heat needed to raise the temperature of 1 kg of substance by 1°C without phase change.
• Specific Latent Heat of Fusion: Heat required to change 1 kg of substance from solid to liquid without changing temperature.
• Specific Latent Heat of Vaporization: Heat required to change 1 kg of substance from liquid to gas without changing temperature.
• Internal Energy: Total energy of a system (kinetic & potential) of particles.
• First Law of Thermodynamics: Change in internal energy = Heat added to the system minus work done by the system.

Current of Electricity

• Electric Current: Rate of flow of charge. Unit is Amps (A).
• Coulomb: Unit of charge.
• Potential Difference: Energy per unit charge converted to other forms. Measured in Volts (V).
• Volt (V): Potential difference when 1 joule of energy is converted to other forms when 1 coulomb of charge passes through a given point.
• Electromotive Force (EMF): Energy per unit charge supplied by a source to move charges through a circuit.
• Resistance: Ratio of potential difference to current. Measured in Ohms (Ω)
• Ohm (Ω): Resistance of a conductor with a 1V potential difference causing 1A of current to flow.
• Ohm's Law: Current through a metallic conductor is proportional to the potential difference.

Electric Field

• Coulomb's Law: Electric force is proportional to the product of the charges and inversely proportional to the square of the distance between them.
• Electric Field: A region of space where a charge experiences an electric force.
• Electric Field Strength: Electric force per unit positive charge.

Electromagnetism

• Magnetic Field: A region of space where a magnetic material, a current-carrying conductor, or a moving charge experiences a magnetic force.
• Magnetic Flux Density: Magnetic force per unit length of a long straight current-carrying conductor placed at right angles to the magnetic field; measured in Tesla (T).
• Tesla: Uniform magnetic flux density acting normally on a long straight current-carrying wire.

Electromagnetic Induction

• Faraday's Law: Induced EMF is proportional to the rate of change of magnetic flux linkage.
• Magnetic Flux: Product of magnetic flux density and area normal to the flux.
• Magnetic Flux Linkage: Product of magnetic flux and number of turns.
• Weber (Wb): Magnetic flux.
• Lenz's Law: Induced current flows to oppose the change in magnetic flux.

Alternating Currents

• Alternating Current (AC): Current that changes direction periodically.
• Root-Mean-Square (RMS) Value: Equivalent steady direct current or voltage that produces the same heating effect.
• Ideal Transformer: No energy loss in stepping voltages up or down. Primary and Secondary (Turns Ratios)

Quantum Physics

• Photoelectric Effect: Ejection of electrons from a metal surface by incident electromagnetic radiation.
• Threshold Frequency: Minimum frequency for electron emission.
• Photon: A quantum of electromagnetic energy.
• Work Function: Minimum energy needed for an electron to escape the metal surface.
• Stopping Potential: Potential needed to stop the emitted electrons.
• Ionisation Energy: Minimum energy needed to remove an electron from an atom.
• Heisenberg Uncertainty Principle: Cannot know both position and momentum of a particle with perfect accuracy simultaneously.

Nuclear Physics

• Nucleons: Protons and neutrons in the atomic nucleus.
• Nucleon Number: Total number of protons and neutrons in an atom.
• Atomic Number: Number of protons.
• Neutron Number: Number of neutrons.
• Nuclide: Nucleus with a specific number of protons and neutrons.
• Isotope: Atoms of the same element with different numbers of neutrons.
• Atomic Mass Unit (u): 1/12 the mass of a carbon-12 atom.
• Mass Defect: Difference between the mass of a nucleus and the sum of its individual nucleons.
• Binding Energy: Energy required to break a nucleus into its constituent nucleons.
• Binding Energy per Nucleon: Average energy required to remove a nucleon.
• Nuclear Fission: Splitting of a heavy nucleus into lighter nuclei
• Nuclear Fusion: Combination of light nuclei into a heavier nucleus.
• Radioactive Decay: Spontenous and random change in an unstable nucleus to a more stable one by emitting radiation or particles.

Radioactive Decay

• Spontaneous Decay: Decay not triggered by external factors; rate unaffected by environmental conditions..
• Random Decay: Cannot predict when a specific atom will decay, but probability per unit time is constant for that sample.
• Decay Law: Decay rate for a large number of atoms is proportional to the number of undecayed nuclei.
• Half-Life: Time needed for half the nuclei in a sample to decay.
• Activity: Number of nuclear disintegrations/unit time.
• Decay Constant: Probability a nucleus will decay in unit time.
• Count Rate: Rate at which emissions from a radioactive source are detected.